Results 11 to 20 of about 6,774 (89)
Almost simplicial polytopes: the lower and upper bound theorems [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 this is an extended abstract of the full version. We study n-vertex d-dimensional polytopes with at most one nonsimplex facet with, say, d + s vertices, called almost simplicial polytopes.
Eran Nevo +3 more
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Symmetric Fundamental Expansions to Schur Positivity [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 We consider families of quasisymmetric functions with the property that if a symmetric function f is a positive sum of functions in one of these families, then f is necessarily a positive sum of Schur functions.
Austin Roberts
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Hook formulas for skew shapes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 The celebrated hook-length formula gives a product formula for the number of standard Young tableaux of a straight shape. In 2014, Naruse announced a more general formula for the number of standard Young tableaux of skew shapes as a positive sum over ...
Alejandro H. Morales +2 more
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The Smith normal form distribution of a random integer matrix [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 We show that the density μ of the Smith normal form (SNF) of a random integer matrix exists and equals a product of densities μps of SNF over Z/psZ with p a prime and s some positive integer.
Yinghui Wang, Richard P. Stanley
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On (non-) freeness of some tridendriform algebras [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 We present some results on the freeness or non freeness of some tridendriform algebras. In particular, we give a combinatorial proof of the freeness of WQSym, an algebra based on packed words, result already known with an algebraic proof.
Vincent Vong
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Discrete Mathematics & Theoretical Computer Science, 2020 The main objects of noncrossing Catalan combinatorics associated to a finite Coxeter system are noncross- ing partitions, sortable elements, and cluster complexes. The first and the third of these have known Fuss–Catalan generalizations.
Christian Stump +2 more
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An equivalence of multistatistics on permutations [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 We prove a conjecture of J.-C. Novelli, J.-Y. Thibon, and L. K. Williams (2010) about an equivalence of two triples of statistics on permutations. To prove this conjecture, we construct a bijection through different combinatorial objects, starting with a
Arthur Nunge
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Extending the weak order on Coxeter groups [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 We introduce a new family of complete lattices, arising from a digraph together with a valuation on its vertices and generalizing a previous construction of the author.
Francois Viard
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The twist for positroids [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 There are two reasonable ways to put a cluster structure on a positroid variety. In one, the initial seed is a set of Plu ̈cker coordinates. In the other, the initial seed consists of certain monomials in the edge weights of a plabic graph.
Greg Muller, David E. Speyer
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Brick polytopes, lattices and Hopf algebras [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 Generalizing the connection between the classes of the sylvester congruence and the binary trees, we show that the classes of the congruence of the weak order on Sn defined as the transitive closure of the rewriting rule UacV1b1 ···VkbkW ≡k UcaV1b1 ...
Vincent Pilaud
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