F\"uredi-Hajnal and Stanley-Wilf conjectures in higher dimensions

In this paper we discuss analogs of Füredi–Hajnal and Stanley–Wilf conjectures for t-dimensional matrices with t ą 2. 2012 ACM Subject Classification Mathematics of computing Ñ Combinatorics; Mathematics of computing Ñ Combinatoric problems; Mathematics of computing Ñ Permutations and combinations

[1]  Rémi Watrigant,et al.  Twin-width II: small classes , 2020, SODA.

[2]  Jaroslav Nesetril,et al.  Twin-width and permutations , 2021, ArXiv.

[3]  Zoltán Füredi,et al.  Davenport-Schinzel theory of matrices , 1992, Discret. Math..

[4]  Zoltán Füredi,et al.  Shadows of colored complexes. , 1988 .

[5]  Eun Jung Kim,et al.  Twin-width I: tractable FO model checking , 2020, 2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS).

[6]  Nathan Linial,et al.  An upper bound on the number of high-dimensional permutations , 2011, Comb..

[7]  Patrice Ossona de Mendez,et al.  TWIN-WIDTH IV: LOW COMPLEXITY MATRICES , 2021 .

[8]  Louis J. Billera,et al.  Face Numbers of Polytopes and Complexes , 2004, Handbook of Discrete and Computational Geometry, 2nd Ed..

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

[10]  Pierre Simon,et al.  Ordered graphs of bounded twin-width , 2021, ArXiv.

[11]  Martin Klazar,et al.  The Füredi-Hajnal Conjecture Implies the Stanley-Wilf Conjecture , 2000 .

[12]  Rémi Watrigant,et al.  Twin-width III: Max Independent Set and Coloring , 2020, ArXiv.