Results 11 to 20 of about 89 (79)
A bijective proof of Kohnert's rule for Schubert polynomials [PDF]
, 2022 Kohnert proposed a formula for Schubert polynomials as the generating polynomial for certain unit cell diagrams obtained from the diagram of a permutation.
Assaf, Sami H.
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Toppleable permutations, excedances and acyclic orientations [PDF]
, 2022 Recall that an excedance of a permutation \(\pi\) is any position \(i\) such that \(\pi_i > i\). Inspired by the work of Hopkins, McConville and Propp (Elec. J. Comb., 2017) on sorting using toppling, we say that a permutation is toppleable if it gets
Hathcock, Daniel +2 more
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No extremal square-free words over large alphabets [PDF]
, 2022 A word is square-free if it does not contain any square (a word of the form \(XX\)), and is extremal square-free if it cannot be extended to a new square-free word by inserting a single letter at any position.
Zhang, Shengtong, Hong, Letong
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Odd diagrams, Bruhat order, and pattern avoidance [PDF]
, 2022 The odd diagram of a permutation is a subset of the classical diagram with additional parity conditions. In this paper, we study classes of permutations with the same odd diagram, which we call odd diagram classes.
Brenti, Francesco +2 more
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The Hurwitz action in complex reflection groups [PDF]
, 2022 We enumerate Hurwitz orbits of shortest reflection factorizations of an arbitrary element in the infinite family \(G(m, p, n)\) of complex reflection groups.
Lewis, Joel Brewster, Wang, Jiayuan
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TO TEACH COMBINATORICS, USING SELECTED PROBLEMS [PDF]
, 2012 In 1972, professor Grigore Moisil, the most famous Romanian academician for Mathematics, said about Combinatorics, that it is “an opportunity of a renewed gladness”, because “each problem in the domain asks for its solving, an expenditure without any ...
Modan, Laurentiu
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Counting lattice paths by crossings and major index I: the corner-flipping bijections [PDF]
, 2022 We solve two problems regarding the enumeration of lattice paths in \(\mathbb{Z}^2\) with steps \((1,1)\) and \((1,-1)\) with respect to the major index, defined as the sum of the positions of the valleys, and to the number of certain crossings.
Elizalde, Sergi
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Chain enumeration, partition lattices and polynomials with only real roots [PDF]
, 2023 The coefficients of the chain polynomial of a finite poset enumerate chains in the poset by their number of elements. The chain polynomials of the partition lattices and their standard type \(B\) analogues are shown to have only real roots.
Kalampogia-Evangelinou, Katerina +1 more
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Some convolution identities for Frobenius-Euler polynomials [PDF]
, 2017 In this paper, by applying the generating function methods and summation transform techniques, we establish some new convolution identities for the Frobenius-Euler polynomials. It turns out that some well-known results are obtained as special cases.
Jing Pan +3 more
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An asymptotically tight lower bound for superpatterns with small alphabets [PDF]
, 2023 A permutation \(\sigma \in S_n\) is a \(k\)-superpattern (or \(k\)-universal) if it contains each \({\tau \in S_k}\) as a pattern. This notion of "superpatterns" can be generalized to words on smaller alphabets, and several questions about superpatterns ...
Hunter, Zach
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