The Tutte Polynomial Part I: General Theory
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[1] J. H. Mason,et al. Matroids as the Study of Geometrical Configurations , 1977 .
[2] James G. Oxley,et al. On a matroid identity , 1983, Discret. Math..
[3] Dominic Welsh,et al. ON SOME PERCOLATION RESULTS OF J. M. HAMMERSLEY , 1979 .
[4] Tom Brylawski,et al. An Affine Representation for Transversal Geometries , 1975 .
[5] T. A. Dowling,et al. The slimmest geometric lattices , 1974 .
[6] S. Cardy. The proof of, and generalisations to, a conjecture by Baker and Essam , 1973, Discret. Math..
[7] G. Rota. On the Foundations of Combinatorial Theory , 2009 .
[8] Thomas Zaslavsky,et al. Combinatorial Geometries: The Möbius Function and the Characteristic Polynomial , 1987 .
[9] J. Macwilliams. A theorem on the distribution of weights in a systematic code , 1963 .
[10] G. Szekeres,et al. An inequality for the chromatic number of a graph , 1968 .
[11] Thomas A. Dowling,et al. A class of geometric lattices based on finite groups , 1973 .
[12] Paul D. Seymour,et al. Nowhere-zero 6-flows , 1981, J. Comb. Theory, Ser. B.
[13] Thomas H. Brylawski,et al. Hyperplane reconstruction of the Tutte polynomial of a geometric lattice , 1981, Discret. Math..
[14] Andrea Brini,et al. A Class of Rank-invariants for Perfect Matroid Designs , 1980, Eur. J. Comb..
[15] G. Rota,et al. On The Foundations of Combinatorial Theory: Combinatorial Geometries , 1970 .
[16] Daniel J. Kleitman,et al. Normalized Matching in Direct Products of Partial Orders , 1973 .
[17] Michel Las Vergnas,et al. On the Tutte Polynomial of a Morphism of Matroids , 1980 .
[18] Richard P. Stanley. Acyclic orientations of graphs , 1973, Discret. Math..
[19] J. Kahn,et al. Varieties and universal models in the theory of combinatorial geometries , 1980 .
[20] Thomas Zaslavsky. Orientation of Signed Graphs , 1991, Eur. J. Comb..
[21] Thomas Zaslavsky. Maximal Dissections of a Simplex , 1976, J. Comb. Theory, Ser. A.
[22] James Oxley,et al. Matroids whose ground sets are domains of functions , 1982, Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics.
[23] Michel Las Vergnas,et al. Acyclic and totally cyclic orientations of combinatorial geometries , 1977, Discret. Math..
[24] D. Welsh,et al. Combinatorial applications of an inequality from statistical mechanics , 1975, Mathematical Proceedings of the Cambridge Philosophical Society.
[25] Kenneth Baclawski,et al. Whitney Numbers of Geometric Lattices , 1975 .
[26] G. Rota,et al. Studies in combinatorics , 1980 .
[27] Tom Brylawski. Intersection theory for graphs , 1981, J. Comb. Theory, Ser. B.
[28] Hassler Whitney,et al. The Coloring of Graphs , 1932 .
[29] Tom Brylawski,et al. A combinatorial model for series-parallel networks , 1971 .
[30] Pierre Martin,et al. Remarkable valuation of the dichromatic polynomial of planar multigraphs , 1978, J. Comb. Theory, Ser. B.
[31] Pierre Martin,et al. Enumérations eulériennes dans les multigraphes et invariants de Tutte-Grothendieck , 1977 .
[32] Dominic Welsh,et al. Surveys in Combinatorics: Colouring problems and matroids , 1979 .
[33] T. Zaslavsky. Facing Up to Arrangements: Face-Count Formulas for Partitions of Space by Hyperplanes , 1975 .
[34] Michel Las Vergnas,et al. The Tutte Polynomial of a Morphism of Matroids 6. A Multi-Faceted Counting Formula for Hyperplane Regions and Acyclic Orientations , 2012, 1205.5424.
[35] W. T. Tutte. On the algebraic theory of graph colorings , 1966 .
[36] Tom Brylawski,et al. The tutte-grothendieck ring , 1972 .
[37] Tom Brylawski,et al. Reconstructing combinatorial geometries , 1974 .
[38] W. D. Wallis,et al. Combinatorial Mathematics VI , 1979 .
[39] Donald E. Knuth,et al. The Asymptotic Number of Geometries , 1974, J. Comb. Theory, Ser. A.
[40] Robert L. Hemminger,et al. Graph reconstruction - a survey , 1977, J. Graph Theory.
[41] G. Birkhoff. A Determinant Formula for the Number of Ways of Coloring a Map , 1912 .
[42] Tom Brylawski,et al. Modular constructions for combinatorial geometries , 1975 .
[43] James G. Oxley,et al. The Broken-circuit Complex: Its Structure and Factorizations , 1981, Eur. J. Comb..
[44] R. Read. An introduction to chromatic polynomials , 1968 .
[45] James G. Oxley,et al. Several identities for the characteristic polynomial of a combinatorial geometry , 1980, Discret. Math..
[46] Tom Brylawski,et al. A combinatorial perspective on the Radon convexity theorem , 1976 .
[47] N. Biggs. Algebraic Graph Theory , 1974 .
[48] Thomas Zaslavsky,et al. Signed graph coloring , 1982, Discret. Math..
[49] Beniamino Segre,et al. Lectures on modern geometry , 1962 .
[50] T. Zaslavsky. The slimmest arrangements of hyperplanes: II. Basepointed geometric lattices and Euclidean arrangements , 1981 .
[51] James Oxley,et al. COLOURING, PACKING AND THE CRITICAL PROBLEM , 1978 .
[52] Thomas Zaslavsky,et al. Chromatic invariants of signed graphs , 1982, Discret. Math..
[53] Tom Brylawski. On the nonreconstructibility of combinatorial geometries , 1975 .
[54] H. Whitney. 2-Isomorphic Graphs , 1933 .
[55] Richard P. Stanley,et al. Modular elements of geometric lattices , 1971 .
[56] Henry H. Crapo. Möbius Inversion in Lattices , 1969 .
[57] John W. Essam,et al. Graph theory and statistical physics , 1971, Discret. Math..
[58] William T. Tutte. A Ring in Graph Theory , 1947 .
[59] W. T. Tutte,et al. A Contribution to the Theory of Chromatic Polynomials , 1954, Canadian Journal of Mathematics.
[60] W. T. Tutte. Matroids and graphs , 1959 .
[61] F. Jaeger,et al. Flows and generalized coloring theorems in graphs , 1979, J. Comb. Theory, Ser. B.
[62] H. Crapo. A higher invariant for matroids , 1967 .
[63] Alexander Rosa,et al. Steiner quadruple systems - a survey , 1978, Discret. Math..
[64] Alexander Schrijver,et al. The Blocking Number of an Affine Space , 1978, J. Comb. Theory, Ser. A.
[65] R. Bixby,et al. A composition for matroids , 1975 .
[66] David K. Arrowsmith,et al. On the enumeration of chains in regular chain-groups , 1982, J. Comb. Theory, Ser. B.
[67] Results and Problems in Galois Geometry , 1980 .
[68] G. C. Shephard. Combinatorial Properties of Associated Zonotopes , 1974, Canadian Journal of Mathematics.
[69] Gian-Carlo Rota,et al. Some Problems in Combinatorial Geometry , 1973 .
[70] J. A. Bondy,et al. Graph Theory with Applications , 1978 .
[71] James Oxley,et al. A generalization of a covering problem of mullin and stanton for matroids , 1979 .
[72] M. Deza. On Perfect Matroid Designs (デザインの構成と解析) , 1977 .
[73] R. Winder. Partitions of N-Space by Hyperplanes , 1966 .
[74] Joseph P. S. Kung,et al. Coherent orientations and series-parallel networks , 1980, Discret. Math..
[75] Dominic Welsh,et al. On the chromatic number of binary matroids , 1980 .
[76] Tom Brylawski,et al. Intersection Theory for Embeddings of Matroids into Uniform Geometries , 1979 .
[77] Michel Deza,et al. Some Properties of Perfect Matroid Designs , 1980 .
[78] H. Crapo,et al. The Tutte polynomial , 1969, 1707.03459.
[79] James G. Oxley,et al. On a covering problem of Mullin and Stanton for binary matroids , 1979 .
[80] Michel Las Vergnas,et al. Orientability of matroids , 1978, J. Comb. Theory, Ser. B.
[81] Paul Seymour,et al. On Tutte's extension of the four-colour problem , 1981, J. Comb. Theory, Ser. B.
[82] Anders Björner,et al. Some matroid inequalities , 1980, Discret. Math..
[83] A. Barlotti. Some topics in finite geometrical structures , 1965 .
[84] H. Crapo,et al. The Möbius function of a lattice , 1966 .
[85] Curtis Greene,et al. An Inequality for the Mobius Function of a Geometric Lattice , 1975 .
[86] D. Lucas,et al. Weak maps of combinatorial geometries , 1975 .
[87] W. T. Tutte. Lectures on matroids , 1965 .
[88] Thomas Zaslavsky,et al. The Geometry of Root Systems and Signed Graphs , 1981 .
[89] H. Whitney. On the Abstract Properties of Linear Dependence , 1935 .
[90] Tom Brylawski. A Determinantal Identity for Resistive Networks , 1977 .
[91] Paul D. Seymour,et al. Decomposition of regular matroids , 1980, J. Comb. Theory, Ser. B.
[92] James G. Oxley,et al. On cographic regular matroids , 1979, Discret. Math..
[93] C. Greene. Weight Enumeration and the Geometry of Linear Codes , 1976 .
[94] Curtis Greenl,et al. On the Möbius algebra of a partially ordered set , 1973 .
[95] Gian-Carlo Rota,et al. THE NUMBER OF SUBSPACES OF A VECTOR SPACE. , 1969 .
[96] Anders Björner,et al. On the homology of geometric lattices , 1982 .
[97] W. T. Tutte. A Class Of Abelian Groups , 1956, Canadian Journal of Mathematics.
[98] W. T. Tutte,et al. On dichromatic polynomials , 1967 .
[99] Dominic Welsh,et al. Euler and bipartite matroids , 1969 .
[100] James Oxley,et al. On Crapo's Beta Invariant for Matroids , 1982 .
[101] James Oxley,et al. Cocircuit coverings and packings for binary matroids , 1978 .
[102] G. Dirac. A Property of 4-Chromatic Graphs and some Remarks on Critical Graphs , 1952 .
[103] Thomas H. Brylawski. Some properties of basic families of subsets , 1973, Discret. Math..
[104] D. Lucas. Properties of rank preserving weak maps , 1974 .
[105] Raul Cordovil,et al. Euler's relation, möbius functions and matroid identities , 1982 .
[106] A. A. Bruen,et al. Blocking Sets in Affine Planes , 1983 .
[107] Tom Brylawski,et al. Matroids and combinatorial geometries , 1980 .
[108] Thomas Zaslavsky,et al. Counting the faces of cut-up spaces , 1975 .
[109] T. A. Dowling. A q-Analog of the Partition Lattice††t The research reported here was partially supported by the Air Force Office of Scientific Research under Contract AFOSR-68-1415. , 1973 .
[110] Tom Brylawski,et al. Connected matroids with the smallest whitney numbers , 1977, Discret. Math..
[111] H. Whitney. A logical expansion in mathematics , 1932 .
[112] Tom Brylawski. The broken-circuit complex , 1977 .
[113] K. Baclawski. The Möbius algebra as a Grothendieck ring , 1979 .
[114] Thomas Zaslavsky,et al. ON THE INTERPRETATION OF WHITNEY NUMBERS THROUGH ARRANGEMENTS OF HYPERPLANES, ZONOTOPES, NON-RADON PARTITIONS, AND ORIENTATIONS OF GRAPHS , 1983 .
[115] Thomas A. Dowling,et al. Codes, packings and the critical problem , 1971 .
[116] G. Rota. On the foundations of combinatorial theory I. Theory of Möbius Functions , 1964 .
[117] Jacobus H. van Lint,et al. Coding Theory , 1971 .
[118] S. F. Kapoor,et al. The Many Facets of Graph Theory , 1969 .
[119] R. L. Brooks. On Colouring the Nodes of a Network , 1941 .
[120] Raul Cordovil,et al. Sur L'Évaluation t(M; 2, 0) du Polynôme de Tutte d'un Matroïde et une Conjecture de B. Grünbaum Relative aux Arrangements de Droites du Plan , 1980, Eur. J. Comb..
[121] Tom Brylawski,et al. A decomposition for combinatorial geometries , 1972 .
[122] Bernt Lindström,et al. On the chromatic number of regular matroids , 1978, J. Comb. Theory, Ser. B.
[123] D. R. Fulkerson,et al. Transversals and Matroid Partition , 1965 .