Proceedings of the 1st International Conference on Algebras, Graphs and Ordered Sets (ALGOS 2020)

Originating in arithmetics and logic, the theory of ordered sets is now a field of combinatorics that is intimately linked to graph theory, universal algebra and multiple-valued logic, and that has a wide range of classical applications such as formal calculus, classification, decision aid and social choice. This international conference “Algebras, graphs and ordered set” (ALGOS) brings together specialists in the theory of graphs, relational structures and ordered sets, topics that are omnipresent in artificial intelligence and in knowledge discovery, and with concrete applications in biomedical sciences, security, social networks and e-learning systems. One of the goals of this event is to provide a common ground for mathematicians and computer scientists to meet, to present their latest results, and to discuss original applications in related scientific fields. On this basis, we hope for fruitful exchanges that can motivate multidisciplinary projects. The first edition of ALgebras, Graphs and Ordered Sets (ALGOS 2020) has a particular motivation, namely, an opportunity to honour Maurice Pouzet on his 75th birthday! For this reason, we have particularly welcomed submissions in areas related to Maurice’s many scientific interests: • Lattices and ordered sets • Combinatorics and graph theory • Set theory and theory of relations • Universal algebra and multiple valued logic • Applications: formal calculus, knowledge discovery, biomedical sciences, decision aid and social choice, security, social networks, web semantics...

[1]  M. Grabisch,et al.  On integer-valued means and the symmetric maximum , 2017 .

[2]  Mariusz Wozniak,et al.  A note on embedding graphs without short cycles , 2004, Discret. Math..

[3]  Miguel Couceiro,et al.  Every quasitrivial n-ary semigroup is reducible to a semigroup , 2019, Algebra universalis.

[4]  Countably Complementable,et al.  LINEAR ORDERINGS , 2006 .

[5]  Timothy Bourke,et al.  Mechanized semantics and verified compilation for a dataflow synchronous language with reset , 2019, Proc. ACM Program. Lang..

[6]  Gregory Gutin,et al.  Digraphs - theory, algorithms and applications , 2002 .

[7]  Michael C. Laskowski,et al.  The uncountable spectra of countable theories , 2000, math/0007199.

[8]  B. A. Romov.  The algebras of partial functions and their invariants , 1981 .

[9]  Gábor J. Székely,et al.  Integer valued means , 2014 .

[10]  P. Hilton,et al.  Catalan Numbers, Their Generalization, and Their Uses , 1991 .

[11]  Grzegorz Rozenberg,et al.  Handbook of Graph Grammars and Computing by Graph Transformations, Volume 1: Foundations , 1997 .

[12]  Natasha Dobrinen.  The Ramsey theory of the universal homogeneous triangle-free graph , 2020, J. Math. Log..

[13]  G. Huet,et al.  Equations and rewrite rules: a survey , 1980 .

[14]  Jean-Pierre Jouannaud,et al.  Drags: A compositional algebraic framework for graph rewriting , 2019, Theor. Comput. Sci..

[15]  Noga Alon,et al.  Ranking Tournaments , 2006, SIAM J. Discret. Math..

[16]  Joris van der Hoeven,et al.  Transseries and Real Differential Algebra , 2006 .

[17]  Michel Grabisch,et al.  The Möbius transform on symmetric ordered structures and its application to capacities on finite sets , 2004, Discret. Math..

[18]  Daniel Meister,et al.  Recognition and computation of minimal triangulations for AT-free claw-free and co-comparability graphs , 2005, Discret. Appl. Math..

[19]  P. Bois-Reymond.  Ueber asymptotische Werthe, infinitäre Approximationen und infinitäre Auflösung von Gleichungen , 1875 .

[20]  Rolf Niedermeier,et al.  Linear-Time Algorithm for Maximum-Cardinality Matching on Cocomparability Graphs , 2017, SIAM J. Discret. Math..

[21]  Nicolas M. Thi'ery,et al.  The orbit algebra of a permutation group with polynomial profile is Cohen-Macaulay. , 2018, 1804.03489.

[22]  Dragan Masulovic.  Pre-adjunctions and the Ramsey property , 2018, Eur. J. Comb..

[23]  Andrzej Ehrenfeucht,et al.  Primitivity is Hereditary for 2-Structures , 1990, Theor. Comput. Sci..

[25]  Timothy Bourke,et al.  A formally verified compiler for Lustre , 2017, PLDI.

[26]  G. N. Raney.  Functional composition patterns and power series reversion , 1960 .

[27]  Steffen Staab,et al.  On the Influence of Description Logics Ontologies on Conceptual Similarity , 2008, EKAW.

[28]  Kathryn Fraughnaugh,et al.  Introduction to graph theory , 1973, Mathematical Gazette.

[29]  Heiko Paulheim,et al.  Feature Selection in Hierarchical Feature Spaces , 2014, Discovery Science.

[30]  William M. Kantor,et al.  On incidence matrices of finite projective and affine spaces , 1972 .

[31]  Spin Multiplicities , 2016, 1607.05849.

[32]  D. Geiger.  CLOSED SYSTEMS OF FUNCTIONS AND PREDICATES , 1968 .

[33]  Helmut Länger.  The free algebra in the variety generated by quasi-trivial semigroups , 1980 .

[34]  Filip De Turck,et al.  Inducing a Decision Tree with Discriminative Paths to Classify Entities in a Knowledge Graph , 2019, SEPDA@ISWC.

[35]  Derek G. Corneil,et al.  A Unified View of Graph Searching , 2008, SIAM J. Discret. Math..

[36]  Imre Bárány,et al.  Notes About the Carathéodory Number , 2012, Discrete & Computational Geometry.

[37]  Rudolf Halin,et al.  Miscellaneous problems on infinite graphs , 2000, J. Graph Theory.

[38]  H. Belbachir,et al.  Les nombres de Stirling associés avec succession d'ordre 2, nombres de Fibonacci–Stirling et unimodalité , 2015 .

[39]  Steven de Rooij,et al.  Substructure counting graph kernels for machine learning from RDF data , 2015, J. Web Semant..

[40]  H. D. Macpherson.  Growth rates in infinite graphs and permutation groups , 1985 .

[41]  Wilhelm Dörnte.  Untersuchungen über einen verallgemeinerten Gruppenbegriff , 1929 .

[42]  Sebastian Padó,et al.  Modeling Paths for Explainable Knowledge Base Completion , 2019, ACL 2019.

[43]  Richard P. Stanley,et al.  Some Aspects of Groups Acting on Finite Posets , 1982, J. Comb. Theory, Ser. A.

[44]  G. Mullen,et al.  D-Dimensional hypercubes and the Euler and MacNeish conjectures , 1995 .

[45]  Natasha Dobrinen.  The Ramsey Theory of Henson graphs , 2019 .

[46]  E. Cohen,et al.  From entanglement witness to generalized Catalan numbers , 2015, Scientific Reports.

[47]  A. D. Moivre.  The Doctrine of Chances , 2016, The Doctrine of Chances.

[48]  M. Pouzet,et al.  Boolean sum of graphs and reconstruction up to complementation , 2013 .

[49]  R. Möhring.  Algorithmic Aspects of Comparability Graphs and Interval Graphs , 1985 .

[50]  Max Pitz.  A note on minor antichains of uncountable graphs , 2020, J. Graph Theory.

[51]  M. Bálek,et al.  Large Networks and Graph Limits , 2022 .

[52]  R. Stanley.  Log‐Concave and Unimodal Sequences in Algebra, Combinatorics, and Geometry a , 1989 .

[53]  Jónsson posets and unary Jónsson algebras , 2013 .

[54]  Stéphan Thomassé,et al.  On Better-Quasi-Ordering Countable Series-Parallel Orders , 2000 .

[55]  Paul H. Edelman,et al.  Free hyperplane arrangements betweenAn−1 andBn , 1994 .

[56]  P. Cameron,et al.  Oligomorphic permutation groups , 1990 .

[57]  R. Fraïssé.  L'Intervalle En Theorie Des Relations; Ses Generalisations Filtre Intervallaire Et Cloture D'Une Relation , 1984 .

[58]  Max Pitz.  A new obstruction for normal spanning trees , 2020, Bulletin of the London Mathematical Society.

[59]  I. Gessel,et al.  A Combinatorial Interpretation of the Numbers 6 (2n)! =n! (n + 2)! , 2004 .

[60]  Youssef Boudabbous,et al.  Finite Tournaments with a Nonempty Diamonds’ Support , 2013, Graphs Comb..

[61]  R.K. Guy,et al.  On numbers and games , 1978, Proceedings of the IEEE.

[62]  Maurice Pouzet,et al.  Sperner Properties for Groups and Relations , 1986, Eur. J. Comb..

[63]  F. Brenti,et al.  Unimodal, log-concave and Pólya frequency sequences in combinatorics , 1989 .

[64]  J. Howie.  Fundamentals of semigroup theory , 1995 .

[65]  Mark E. Watkins,et al.  Infinite paths that contain only shortest paths , 1986, J. Comb. Theory, Ser. B.

[66]  Bruno Courcelle,et al.  Graph Structure and Monadic Second-Order Logic: Algorithmic applications , 2012 .

[67]  Béla Bollobás,et al.  The unlabelled speed of a hereditary graph property , 2009, J. Comb. Theory, Ser. B.

[68]  Jeremy P. Spinrad,et al.  Between O(nm) and O(nalpha) , 2003, SIAM J. Comput..

[69]  E. Corominas,et al.  On better quasi-ordering countable trees , 1985, Discret. Math..

[70]  Maurice Pouzet,et al.  Representation of ideals of relational structures , 2009, Discret. Math..

[71]  Jan J. M. M. Rutten,et al.  Behavioural differential equations: a coinductive calculus of streams, automata, and power series , 2003, Theor. Comput. Sci..

[72]  Jean Ecalle,et al.  Introduction aux fonctions analysables et preuve constructive de la conjecture de Dulac , 1992 .

[73]  Mariusz Wozniak,et al.  Packing of graphs and permutations--a survey , 2004, Discret. Math..

[74]  Diana Schmidt,et al.  Well-Partial Orderings and their Maximal Order Types , 2020 .

[75]  Dick H. J. Jongh,et al.  Well-partial orderings and hierarchies , 1977 .

[76]  Boris I. Plotkin.  Some Results and Problems Related to Universal Algebraic Geometry , 2007, Int. J. Algebra Comput..

[77]  Emil L. Post.  The two-valued iterative systems of mathematical logic , 1942 .

[78]  H. Belbachir,et al.  LINEAR RECURRENT SEQUENCES AND POWERS OF A SQUARE MATRIX , 2006 .

[79]  P. Dedecker.  Review: Roland Fraisse, Sur Quelques Classifications des Systemes de Relations , 1957 .

[80]  P. Cameron.  Orbits of Permutation Groups on Unordered Sets, III: Imprimitive Groups , 1983 .

[81]  Sadjia Abbad,et al.  Companion sequences associated to ther-Fibonacci sequence: algebraic andcombinatorial properties , 2019, TURKISH JOURNAL OF MATHEMATICS.

[82]  L. Santocanale,et al.  Free μ-lattices , 2000 .

[83]  Djamila Oudrar.  Sur l'énumération de structures discrètes, une approche par la théorie des relations , 2016 .

[84]  Béla Bollobás,et al.  Hereditary properties of combinatorial structures: Posets and oriented graphs , 2007, J. Graph Theory.

[85]  Athena Sparks.  On the number of clonoids , 2018, Algebra universalis.

[86]  Kazuhiro Suzuki.  A Counterexample to a Conjecture on Packing Two Copies of a Tree into its Third Power , 2004, Ars Comb..

[87]  Abraham Robinson,et al.  On the metamathematics of algebra , 1963 .

[88]  E. Tóth,et al.  On the shape of solution sets of systems of (functional) equations , 2017 .

[89]  Jean-Luc Marichal,et al.  Characterizations of quasitrivial symmetric nondecreasing associative operations , 2017, Semigroup Forum.

[90]  P. M. Cohn,et al.  THE METAMATHEMATICS OF ALGEBRAIC SYSTEMS , 1972 .

[92]  Ekkehard Köhler,et al.  On the Power of Graph Searching for Cocomparability Graphs , 2016, SIAM J. Discret. Math..

[93]  V. Pestov,et al.  Fraïssé Limits, Ramsey Theory, and topological dynamics of automorphism groups , 2003 .

[94]  Maurice Pouzet,et al.  Relation Minimale Pour Son Ǎge , 1979, Math. Log. Q..

[95]  Heiko Paulheim,et al.  Semantic Web in data mining and knowledge discovery: A comprehensive survey , 2016, J. Web Semant..

[96]  Dragan Mašulović,et al.  Homomorphism-homogeneous monounary algebras , 2013 .

[97]  Serge Abiteboul,et al.  PARIS: Probabilistic Alignment of Relations, Instances, and Schema , 2011, Proc. VLDB Endow..

[98]  Dwight Duffus,et al.  Symmetric Chain Decompositions of Quotients by Wreath Products , 2015, Electron. J. Comb..

[99]  Houmem Belkhechine.  Indécomposabilité des graphes et des tournois , 2009 .

[100]  John E. Freund,et al.  Restricted Occupancy Theory—A Generalization of Pascal's Triangle , 1956 .

[101]  Peter J. Cameron,et al.  On an algebra related to orbit-counting , 1998 .

[102]  M. Pouzet,et al.  Application d'une propriété combinatoire des parties d'un ensemble aux groupes et aux relations , 1976 .

[103]  L. Chambadal,et al.  Fonctions d'une variable rèelle , 1972 .

[104]  Youssef Boudabbous,et al.  3-minimal Triangle-free Graphs , 2014, Discret. Math..

[105]  Ralph P. Grimaldi,et al.  Fibonacci and Catalan Numbers: An Introduction , 2012 .

[106]  Mike D. Atkinson,et al.  Simple permutations and pattern restricted permutations , 2005, Discret. Math..

[107]  T. Koshy.  Catalan Numbers with Applications , 2008 .

[108]  Hélène Kirchner,et al.  Strategic port graph rewriting: an interactive modelling framework , 2018, Mathematical Structures in Computer Science.

[109]  Vincent Vatter.  Small permutation classes , 2007, 0712.4006.

[110]  Horst Wegner.  On the Location of the Maximum Stirling Number(s) of the Second Kind , 2009 .

[111]  Maurice Pouzet,et al.  Application de la Notion de Relation Presque-Enchainable au Denombrement des Restrictions Finies D'une Relation , 1981, Math. Log. Q..

[113]  Imed Boudabbous,et al.  Indecomposable tournaments and their indecomposable subtournaments on 5 and 7 vertices , 2013, Ars Comb..

[114]  Richard Laver,et al.  On Fraisse's order type conjecture , 1971 .

[115]  Amedeo Napoli,et al.  PGxO and PGxLOD: a reconciliation of pharmacogenomic knowledge of various provenances, enabling further comparison , 2018 .

[116]  C. Nash-Williams.  On well-quasi-ordering infinite trees , 1963, Mathematical Proceedings of the Cambridge Philosophical Society.

[117]  Andy Zucker.  Big Ramsey degrees and topological dynamics , 2018, Groups, Geometry, and Dynamics.

[118]  Joaquín Pascual,et al.  Infinite Abelian Groups , 1970 .

[119]  Maurice Pouzet,et al.  A generalized permutahedron , 1995 .

[120]  N.W. Sauer.  Distance Sets of Urysohn Metric Spaces , 2013, Canadian Journal of Mathematics.

[121]  James Geller,et al.  Raising, to Enhance Rule Mining in Web Marketing with the Use of an Ontology , 2008 .

[123]  Dominique Perrin,et al.  Finite and infinite words , 2002 .

[124]  Miklós Bóna,et al.  Combinatorics of permutations , 2022, SIGA.

[126]  Thomas R. Gruber,et al.  A translation approach to portable ontology specifications , 1993, Knowl. Acquis..

[128]  Maurice Pouzet,et al.  Equimorphy: the case of chains , 2014, Arch. Math. Log..

[129]  Maurice Pouzet,et al.  Hypomorphy of graphs up to complementation , 2006, J. Comb. Theory, Ser. B.

[130]  Bernd I. Dahn,et al.  Notes on exponential-logarithmic terms , 1987 .

[132]  Marcos Aurélio Domingues,et al.  Using Taxonomies to Facilitate the Analysis of the Association Rules , 2011, ArXiv.

[133]  Justine Falque.  Classification des groupes P-oligomorphes, conjectures de Cameron et Macpherson. (Classification of P-oligomorphic groups, conjectures of Cameron and Macpherson) , 2019 .

[134]  Richard P. Stanley,et al.  Weyl Groups, the Hard Lefschetz Theorem, and the Sperner Property , 1980, SIAM J. Algebraic Discret. Methods.

[135]  Detlef Plump,et al.  Simplification Orders for Term Graph Rewriting , 1997, MFCS.

[136]  A. Clifford.  Bands of semigroups , 1954 .

[137]  H. S. Hall,et al.  Higher Algebra: A Sequel to Elementary Algebra for Schools , 1964 .

[138]  M. Potter.  Orders of infinity , 2004 .

[139]  Gábor Tardos,et al.  Excluded permutation matrices and the Stanley-Wilf conjecture , 2004, J. Comb. Theory, Ser. A.

[140]  Fabian M. Suchanek,et al.  AMIE: association rule mining under incomplete evidence in ontological knowledge bases , 2013, WWW.

[141]  Youssef Boudabbous,et al.  La relation différence et l'anti-isomorphie , 1995, Math. Log. Q..

[142]  R. Graham,et al.  Ramsey’s theorem for $n$-parameter sets , 1971 .

[143]  M. Pouzet.  The Asymptotic Behavior of a Class of Counting Functions , 1980 .

[144]  Jacques Sakarovitch,et al.  Elements of Automata Theory , 2009 .

[145]  Richard M. Karp,et al.  Reducibility Among Combinatorial Problems , 1972, 50 Years of Integer Programming.

[146]  Bruno Guillaume,et al.  Dependency Parsing with Graph Rewriting , 2015, IWPT.

[147]  Anders Yeo,et al.  The Minimum Feedback Arc Set Problem is NP-Hard for Tournaments , 2006, Combinatorics, Probability and Computing.

[148]  Raymond Balbes,et al.  Projective and injective distributive lattices. , 1967 .

[149]  Murat Alp,et al.  Balancing Diophantine triples with distance 1 , 2015, Period. Math. Hung..

[150]  Hacène Belbachir,et al.  Sums of products of generalized Fibonacci and Lucas numbers , 2007, Ars Comb..

[151]  Bruno Courcelle,et al.  The modular decomposition of countable graphs. Definition and construction in monadic second-order logic , 2008, Theor. Comput. Sci..

[152]  Dieter Kratsch,et al.  Domination on Cocomparability Graphs , 1993, SIAM J. Discret. Math..

[153]  Jaroslav Nesetril,et al.  Homomorphism-Homogeneous Relational Structures , 2006, Combinatorics, Probability and Computing.

[154]  R. Fraïssé.  Sur l'extension aux relations de quelques propriétés des ordres , 1954 .

[155]  Claude Frasnay,et al.  Quelques problèmes combinatoires concernant les ordres totaux et les relations monomorphes , 1965 .

[156]  H. Jung,et al.  Wurzelbäume und unendliche Wege in Graphen , 1969 .

[157]  Yves Lafont,et al.  Interaction nets , 1989, POPL '90.

[158]  Vadim V. Lozin,et al.  Labelled Induced Subgraphs and Well-Quasi-Ordering , 2015, Order.

[159]  Luigi Santocanale,et al.  On discrete idempotent paths , 2019, WORDS.

[160]  Michel Grabisch,et al.  On the Poset of Computation Rules for Nonassociative Calculus , 2013, Order.

[161]  Ian M. Hodkinson,et al.  Relational Structures Determined by Their Finite Induced Substructures , 1988, J. Symb. Log..

[162]  Pablo Barceló,et al.  Querying graph patterns , 2011, PODS.

[163]  E. C. Milner.  Basic WQO- and BQO-Theory , 1985 .

[164]  Norbert Polat.  Graphs without isometric rays and invariant subgraph properties, I , 1998, J. Graph Theory.

[165]  Nachum Dershowitz,et al.  A Note on Simplification Orderings , 1979, Inf. Process. Lett..

[166]  A. A. Grau.  Ternary Boolean algebra , 1947 .

[167]  N. J. A. Sloane,et al.  The On-Line Encyclopedia of Integer Sequences , 2003, Electron. J. Comb..

[168]  H. Lakser,et al.  Injective Hulls of Semilattices , 1970, Canadian Mathematical Bulletin.

[169]  L. Dries,et al.  ON NUMBERS, GERMS, AND TRANSSERIES , 2017, Proceedings of the International Congress of Mathematicians (ICM 2018).

[170]  Anthony Bonato,et al.  Mutually embeddable graphs and the tree alternative conjecture , 2006, J. Comb. Theory, Ser. B.

[171]  H. Gonshor.  An Introduction to the Theory of Surreal Numbers , 1986 .

[172]  Béla Bollobás,et al.  Hereditary properties of partitions, ordered graphs and ordered hypergraphs , 2006, Eur. J. Comb..

[173]  L. A. Kaluzhnin,et al.  Galois theory for post algebras. I , 1969 .

[174]  F. Larrión,et al.  Injectivity in varieties of groups , 1982 .

[175]  Maurice Pouzet,et al.  APPLICATIONS OF WELL QUASI-ORDERING AND BETTER QUASI-ORDERING , 1985 .

[176]  Bolyai János Matematikai Társulat,et al.  Algebraic theory of semigroups , 1979 .

[177]  Frank Plumpton Ramsey,et al.  On a Problem of Formal Logic , 1930 .

[178]  Pierre Ille,et al.  Minimal indecomposable graphs , 1998, Discret. Math..

[179]  Robert Brignall,et al.  Permutation Classes of Polynomial Growth , 2006 .

[180]  Nicholas Pippenger,et al.  Galois theory for minors of finite functions , 1998, Discret. Math..

[181]  Tero Harju,et al.  The Theory of 2-Structures - A Framework for Decomposition and Transformation of Graphs , 1997, Handbook of Graph Grammars.

[182]  Gérard Lopez,et al.  Reconstruction of Binary Relations from their Restrictions of Cardinality 2, 3, 4 and (n - 1) I , 1992, Math. Log. Q..

[183]  C. Dubey.  Indecomposable Graphs , .

[184]  Mizuhito Ogawa.  A Note on Algebraic Structure of Tree Decomposition of Graphs , 2000, APLAS.

[185]  Heiko Paulheim,et al.  A Comparison of Propositionalization Strategies for Creating Features from Linked Open Data , 2014, LD4KD.

[186]  Stephen G. Simpson,et al.  A Dual Form of Ramsey's Theorem , 1984 .

[187]  Géraud Sénizergues.  Some Undecidable Termination Problems for Semi-Thue Systems , 1995, Theor. Comput. Sci..

[188]  Bruno Guillaume,et al.  Non-simplifying Graph Rewriting Termination , 2013, TERMGRAPH.

[189]  Maurice Pouzet,et al.  Sandwiches of ages , 2001, Ann. Pure Appl. Log..

[190]  Imed Zaguia,et al.  On Minimal Prime Graphs and Posets , 2008, Order.

[191]  K. B. Reid,et al.  Strongly self-complementary and hereditarily isomorphic tournaments , 1976 .

[192]  Assia Fettouma Tebtoub,et al.  The $t$-successive associated Stirling numbers, $t$-Fibonacci--Stirling numbers, and unimodality , 2017 .

[193]  Hacène Belbachir,et al.  A q-analogue for bisnomial coefficients and generalized Fibonacci sequences , 2014 .

[194]  Steven de Rooij,et al.  A Fast and Simple Graph Kernel for RDF , 2013, DMoLD.

[195]  Huajun Chen,et al.  The Semantic Web , 2011, Lecture Notes in Computer Science.

[196]  Mario Petrich,et al.  Introduction to semigroups , 1973 .

[197]  Maurice Pouzet,et al.  The morphology of infinite tournaments; application to the growth of their profile , 2008, Eur. J. Comb..

[198]  Robert Morris,et al.  Hereditary Properties of Ordered Graphs , 2006 .

[199]  Lionel Nguyen Van Thé.  Ramsey degrees of finite ultrametric spaces, ultrametric Urysohn spaces and dynamics of their isometry groups , 2009, Eur. J. Comb..

[200]  Generalized catalan numbers, sequences and polynomials , 2010 .

[201]  NATHANAEL LEEDOM ACKERMAN.  A CHARACTERIZATION OF QUASITRIVIAL n-SEMIGROUPS , 2013 .

[202]  C. Pech,et al.  On polymorphism-homogeneous relational structures and their clones , 2013, 1305.1159.

[203]  Maurice Pouzet,et al.  Indivisible ultrametric spaces , 2007 .

[204]  Assia Fettouma Tebtoub.  Log-concavity of principal diagonal rays in the regular Lah triangles , 2018, Ars Comb..

[205]  R. Halin,et al.  Über die Maximalzahl fremder unendlicher Wege in Graphen , 1965 .

[206]  Sylvain Kahane,et al.  Word Ordering as a Graph Rewriting Process , 2015, FG.

[207]  Martin Klazar,et al.  On Growth Rates of Closed Permutation Classes , 2003, Electron. J. Comb..

[208]  Gérard Lopez,et al.  L'Indeformabilite des Relations et Multirelations Binaires , 1978, Math. Log. Q..

[209]  G. Meletiou.  Median algebras acting on sets , 1992 .

[210]  Michel Habib,et al.  A new LBFS-based algorithm for cocomparability graph recognition , 2017, Discret. Appl. Math..

[211]  Á. Szendrei,et al.  The submaximal clones on the three-element set with finitely many relative R-classes , 2009, 0905.1614.

[212]  H. Belbachir,et al.  Connection between bi$^{s}$nomial coefficients and their analogs and symmetric functions , 2018 .

[213]  Fabian M. Suchanek,et al.  Canonicalizing Open Knowledge Bases , 2014, CIKM.

[214]  Hacène Belbachir,et al.  Combinatorial identities for the r-Lah numbers , 2014, Ars Comb..

[215]  G. Birkhoff,et al.  A ternary operation in distributive lattices , 1947 .

[216]  P. Hammer,et al.  Aggregation of inequalities in integer programming. , 1975 .

[217]  Hans Zantema,et al.  Matrix Interpretations for Proving Termination of Term Rewriting , 2006, Journal of Automated Reasoning.

[218]  L. Lesieur,et al.  On the eulerian numbers , 1992 .

[219]  The theory of determinants in the historical order of development , 1914 .

[220]  Hacène Belbachir,et al.  Cross recurrence relations for r-Lah numbers , 2013, Ars Comb..

[221]  Maurice Pouzet,et al.  Some Relational Structures with Polynomial Growth and their Associated Algebras I: Quasi-Polynomiality of the Profile , 2006, Electron. J. Comb..

[222]  Robert Brignall,et al.  Decomposing simple permutations, with enumerative consequences , 2008, Comb..

[223]  Heiko Paulheim,et al.  Generating Possible Interpretations for Statistics from Linked Open Data , 2012, ESWC.

[224]  Imed Boudabbous.  Tournaments whose indecomposability graph admits a vertex cover of size 2 , 2016, Ars Comb..

[225]  V. Kandarpa.  On Commutative Δ-Semigroups , 2016 .

[226]  H. Belbachir,et al.  Congruence Properties for Bi$$^s$$snomial Coefficients and Like Extended Ram and Kummer Theorems Under Suitable Hypothesis , 2020 .

[227]  Djamila Oudrar.  Hereditary classes of ordered binary structures , 2019, Advances in Pure and Applied Mathematics.

[228]  A. Björner,et al.  Combinatorics of Coxeter Groups , 2005 .

[229]  Maurice Pouzet,et al.  When is the orbit algebra of a group an integral domain? Proof of a conjecture of P.J. Cameron , 2007, RAIRO Theor. Informatics Appl..

[230]  Tero Harju,et al.  Decompostion of Infinite Labeled 2-Structures , 1994, Results and Trends in Theoretical Computer Science.

[231]  Guy Perrier,et al.  Application of Graph Rewriting to Natural Language Processing , 2018 .

[232]  Ramakrishnan Srikant,et al.  Mining generalized association rules , 1995, Future Gener. Comput. Syst..

[233]  Imre Leader,et al.  The width of downsets , 2019, Eur. J. Comb..

[234]  G. Hardy.  Properties of Logarithmico‐Exponential Functions , 2022 .

[235]  Hamza Si Kaddour,et al.  The (-1)-critically duo-free tournaments , 2015, Ars Comb..

[236]  Weida Tong,et al.  DILIrank: the largest reference drug list ranked by the risk for developing drug-induced liver injury in humans. , 2016, Drug Discovery Today.

[237]  Jean-Pierre Jouannaud,et al.  Rewrite Systems , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[238]  N. Mahadev,et al.  Threshold graphs and related topics , 1995 .

[239]  Tim Weninger,et al.  Discriminative predicate path mining for fact checking in knowledge graphs , 2015, Knowl. Based Syst..

[240]  A. Clifford,et al.  Lectures in semigroups , 1977 .

[241]  Keith R. Milliken,et al.  A Ramsey Theorem for Trees , 1979, J. Comb. Theory, Ser. A.

[242]  William T. Trotter,et al.  Critically indecomposable partially ordered sets, graphs, tournaments and other binary relational structures , 1993, Discret. Math..

[243]  Michel Habib,et al.  LDFS-Based Certifying Algorithm for the Minimum Path Cover Problem on Cocomparability Graphs , 2013, SIAM J. Comput..

[244]  Jean-Pierre Jouannaud,et al.  Graph Path Orderings , 2018, LPAR.

[245]  Maurice Pouzet,et al.  Countable Structures of Given Age , 1992, J. Symb. Log..

[246]  Maurice Pouzet,et al.  The Poset of Copies for Automorphism Groups of Countable Relational Structures , 2020, J. Multiple Valued Log. Soft Comput..

[247]  Joseph B. Kruskal,et al.  The Theory of Well-Quasi-Ordering: A Frequently Discovered Concept , 1972, J. Comb. Theory A.

[248]  Carsten Thomassen,et al.  A Polynomial Algorithm for the 2-Path Problem for Semicomplete Digraphs , 1992, SIAM J. Discret. Math..

[249]  Imed Boudabbous,et al.  Les graphes (-1)-critiques , 2015, Ars Comb..

[250]  John R. Stembridge,et al.  Some permutation representations of weyl groups associated with the cohomology of toric varieties , 1994 .

[251]  P. Rosenstiehl,et al.  Analyse algébrique d'un scrutin , 1963 .

[252]  Tom Roby,et al.  THE LATTICE OF THRESHOLD GRAPHS , 2005 .

[253]  Jitender S. Deogun,et al.  Partially critical indecomposable graphs , 2008, Contributions Discret. Math..

[254]  Sadek Bouroubi,et al.  Connection between ordinary multinomials, Fibonacci numbers, Bell polynomials and discrete uniform distribution. , 2008 .

[255]  Ira M. Gessel,et al.  Super Ballot Numbers , 1992, J. Symb. Comput..

[256]  Béla Bollobás,et al.  Hereditary Properties of Tournaments , 2007, Electron. J. Comb..

[257]  Jørgen Bang-Jensen,et al.  On the problem of finding disjoint cycles and dicycles in a digraph , 2011, Comb..

[258]  Associative idempotent nondecreasing functions are reducible , 2017, Semigroup Forum.

[259]  Graham Higman,et al.  Ordering by Divisibility in Abstract Algebras , 1952 .

[260]  Peter Frankl,et al.  Inequalities for Subsets of a Set and KLYM Posets , 1983 .

[261]  Zohar Manna,et al.  Proving termination with multiset orderings , 1979, CACM.

[262]  Bruce A. Reed,et al.  The gallai-younger conjecture for planar graphs , 1996, Comb..

[263]  Shaun M. Fallat,et al.  The minimum rank of symmetric matrices described by a graph: A survey☆ , 2007 .

[264]  Max Pitz.  Proof of Halin’s normal spanning tree conjecture , 2020, Israel Journal of Mathematics.

[265]  Norbert Sauer.  COLORING SUBGRAPHS OF THE RADO GRAPH , 2006, Comb..

[266]  Hian Poh Yap,et al.  Packing of graphs - a survey , 1988, Discret. Math..

[267]  Igor Dolinka,et al.  Remarks on homomorphism-homogeneous lattices and semilattices , 2011 .

[268]  Alberto Marcone,et al.  Foundations of BQO theory , 1994 .

[269]  N. Shah,et al.  About Pure and Applied Mathematics , 2018 .

[270]  Jimmy Devillet,et al.  On the structure of symmetric n-ary bands , 2021, International Journal of Algebra and Computation.

[271]  Richard P. Stanley,et al.  Quotients of peck posets , 1984 .

[272]  Shiva Kintali,et al.  Forbidden directed minors and Kelly-width , 2017, Theor. Comput. Sci..

[273]  R. Stanley.  An Introduction to Hyperplane Arrangements , 2007 .

[274]  M. Pouzet,et al.  Inversion dans les tournois , 2010, 1007.2103.

[275]  Lionel Nguyen Van Thé,et al.  The Urysohn Sphere Is Oscillation Stable , 2007, 0710.2884.

[276]  George W. Polites,et al.  An introduction to the theory of groups , 1968 .

[277]  Chris D. Godsil,et al.  Chromatic Number and the 2-Rank of a Graph , 2001, J. Comb. Theory B.

[278]  Erkko Lehtonen,et al.  Partial orders induced by quasilinear clones , 2012 .

[279]  M. Sholander.  Medians, lattices, and trees , 1954 .

[280]  Svetlana N. Selezneva,et al.  Polynomial-Time Algorithms for Checking Some Properties of Boolean Functions Given by Polynomials , 2014, Theory of Computing Systems.

[281]  Rolf H. Möhring,et al.  Triangulating Graphs Without Asteroidal Triples , 1996, Discret. Appl. Math..

[282]  Jeremy P. Spinrad,et al.  P4-Trees and Substitution Decomposition , 1992, Discret. Appl. Math..

[283]  Paul D. Seymour,et al.  Graph Minors. XX. Wagner's conjecture , 2004, J. Comb. Theory B.

[284]  Youssef Boudabbous,et al.  (≤k)-reconstructible Binary Relations , 2014, Eur. J. Comb..

[285]  Martin Balko,et al.  Big Ramsey degrees of 3-uniform hypergraphs , 2019, ArXiv.

[286]  Kenneth H. Rosen,et al.  Catalan Numbers , 2002 .

[287]  A. Berarducci,et al.  Surreal numbers, derivations and transseries , 2015, 1503.00315.

[288]  Emily Barnard,et al.  The Canonical Join Complex , 2016, Electron. J. Comb..

[289]  Maurice Pouzet.  The Profile of relations , 2007 .

[290]  Johannes Fürnkranz,et al.  Unsupervised generation of data mining features from linked open data , 2012, WIMS '12.

[291]  Jean-Éric Pin,et al.  Profinite Methods in Automata Theory , 2009, STACS.

[292]  Douglas B. West,et al.  A Symmetric Chain Decomposition of L(4, n) , 1979, Eur. J. Comb..

[293]  Martin Klazar,et al.  Overview of some general results in combinatorial enumeration , 2008, 0803.4292.

[294]  David Garber,et al.  Stirling and Eulerian numbers of types B and D , 2018, GASCom.

[295]  William McCuaig,et al.  Intercyclic digraphs , 1991, Graph Structure Theory.

[296]  Daniel J. Kleitman,et al.  Strong Versions of Sperner's Theorem , 1976, J. Comb. Theory, Ser. A.

[297]  Imed Boudabbous,et al.  Description of the Triangle-free Prime Graphs Having at Most Two Non Critical Vertices , 2020, J. Multiple Valued Log. Soft Comput..

[298]  Timothy Bourke,et al.  A type-based analysis of causality loops in hybrid systems modelers , 2014, HSCC.

[299]  Fabrice Guillet,et al.  Knowledge-Based Interactive Postmining of Association Rules Using Ontologies , 2010, IEEE Transactions on Knowledge and Data Engineering.

[300]  G. Mullen,et al.  Discrete Mathematics Using Latin Squares , 1998, The Mathematical Gazette.

[301]  Ira M. Gessel,et al.  Stirling Polynomials , 1978, J. Comb. Theory, Ser. A.

[302]  Richard Laver,et al.  An Order Type Decomposition Theorem , 1973 .

[303]  Alfred Horn,et al.  The category of semilattices , 1971 .

[304]  Imre Leader,et al.  Normal Spanning Trees, Aronszajn Trees and Excluded Minors , 2001 .

[305]  Philip Ehrlich,et al.  The Rise of non-Archimedean Mathematics and the Roots of a Misconception I: The Emergence of non-Archimedean Systems of Magnitudes , 2006 .

[306]  D. Holt.  Enumerating subgroups of the symmetric group , 2010 .

[307]  David Coudert,et al.  Revisiting Decomposition by Clique Separators , 2018, SIAM J. Discret. Math..

[308]  David P. Williamson,et al.  Primal-Dual Approximation Algorithms for Feedback Problems in Planar Graphs , 1996, Comb..

[309]  J. Rhodes,et al.  Algebraic theory of machines. I. Prime decomposition theorem for finite semigroups and machines , 1965 .

[310]  Guoli Ding,et al.  Subgraphs and well-quasi-ordering , 1992, J. Graph Theory.

[311]  N. Sauer,et al.  Invariant subsets of scattered trees and the tree alternative property of Bonato and Tardif , 2017 .

[312]  Maurice Pouzet,et al.  Divisibility of countable metric spaces , 2007, Eur. J. Comb..

[313]  P. Cameron,et al.  The algebra of an age , 1997 .

[314]  F. Hausdorff,et al.  Grundzüge einer Theorie der geordneten Mengen , 1908 .

[315]  Luigi Santocanale,et al.  The continuous weak order , 2018, Journal of Pure and Applied Algebra.

[316]  Solution sets of systems of equations over finite lattices and semilattices , 2020, 2001.04549.

[317]  Tim Berners-Lee,et al.  Linked Data - The Story So Far , 2009, Int. J. Semantic Web Inf. Syst..

[318]  Heiko Paulheim,et al.  RDF2Vec: RDF Graph Embeddings for Data Mining , 2016, SEMWEB.

[319]  Hamamache Kheddouci,et al.  Packing two copies of a tree into its fourth power , 2000, Discret. Math..

[320]  Martin Klazar.  On Growth Rates of Permutations, Set Partitions, Ordered Graphs and Other Objects , 2008, Electron. J. Comb..

[321]  JEREMIAH CERTAINE,et al.  THE TERNARY OPERATION (abc)±ab-c OF A GROUP , 2007 .

[322]  R. Möhring.  Algorithmic graph theory and perfect graphs , 1986 .

[323]  L. Nguyen Van Th'e,et al.  Structural Ramsey theory of metric spaces and topological dynamics of isometry groups , 2008, 0804.1593.

[324]  W. Hodges.  CLASSIFICATION THEORY AND THE NUMBER OF NON‐ISOMORPHIC MODELS , 1980 .

[325]  R. Diestel,et al.  Normal tree orders for infinite graphs , 1994 .

[326]  L. Dries,et al.  The surreal numbers as a universal $H$-field , 2015, Journal of the European Mathematical Society.

[327]  A. H. Stone.  On σ-Discreteness and Borel Isomorphism , 1963 .

[328]  Jaroslav Nesetril,et al.  First-order limits, an analytical perspective , 2015, Eur. J. Comb..

[329]  Marc Pouzet,et al.  Zélus: a synchronous language with ODEs , 2013, HSCC '13.

[330]  M. Sholander.  Trees, lattices, order, and betweenness , 1952 .

[331]  Jerzy W. Grzymala-Busse,et al.  Automorphisms of Polyadic Automata , 1969, JACM.

[332]  Michel Habib,et al.  Maximal cliques structure for cocomparability graphs and applications , 2016, ArXiv.

[333]  Claude Tardif,et al.  Iterated Arc Graphs , 2016 .

[334]  Charalambos A. Charalambides,et al.  Enumerative combinatorics , 2018, SIGA.

[335]  Z. Farkasová,et al.  Polymorphism-Homogeneous Monounary Algebras , 2015 .

[336]  Erwin Engeler,et al.  Languages with expressions of infinite length , 1966 .

[337]  Pierre Ille,et al.  Indecomposability graph and critical vertices of an indecomposable graph , 2009, Discret. Math..

[338]  David P. Sumner.  Graphs indecomposable with respect to the X-join , 1973, Discret. Math..