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All fields Title Creator / Publisher Keyword Year AND OR AND NOT All fields Title Creator / Publisher Keyword Year AND OR AND NOT All fields Title Creator / Publisher Keyword Year AND OR AND NOT All fields Title Creator / Publisher Keyword Year AND OR AND NOT All fields Title Creator / Publisher Keyword Year Sort by creator [A → Z]' creator [Z → A]' publishing year ↑ (asc)' publishing year ↓ (desc)' title [A → Z]' title [Z → A]' Simple Search Hits 1 – 4 of 4 1 Mahonian STAT on words Kitaev, Sergey; Vajnovszki, Vincent In: ISSN: 0020-0190 ; Information Processing Letters ; https://hal-univ-bourgogne.archives-ouvertes.fr/hal-01418254 ; Information Processing Letters, Elsevier, 2016, 116 (2), pp.157 - 162. ⟨10.1016/j.ipl.2015.09.006⟩ ; http://www.sciencedirect.com/science/article/pii/S0020019015001611 (2016) Abstract: International audience ; In 2000, Babson and Steingrímsson introduced the notion of what is now known as a permutation vincular pattern, and based on it they re-defined known Mahonian statistics and introduced new ones, proving or conjecturing their Mahonity. These conjectures were proved by Foata and Zeilberger in 2001, and by Foata and Randrianarivony in 2006. In 2010, Burstein refined some of these results by giving a bijection between permutations with a fixed value for the major index and those with the same value for STAT , where STAT is one of the statistics defined and proved to be Mahonian in the 2000 Babson and Steingrímsson's paper. Several other statistics are preserved as well by Burstein's bijection. At the Formal Power Series and Algebraic Combinatorics Conference (FPSAC) in 2010, Burstein asked whether his bijection has other interesting properties. In this paper, we not only show that Burstein's bijection preserves the Eulerian statistic ides , but also use this fact, along with the bijection itself, to prove Mahonity of the statistic STAT on words we introduce in this paper. The words statistic STAT introduced by us here addresses a natural question on existence of a Mahonian words analogue of STAT on permutations. While proving Mahonity of our STAT on words, we prove a more general joint equidistribution result involving two six-tuples of statistics on (dense) words, where Burstein's bijection plays an important role. Keyword: [INFO]Computer Science [cs]; Bijections; Combinatorial problems; Combinatorics; Equidistribution; Mathematical Analysis; Mathematical proofs; Pattern; Permutations; Statistic; Words and Permutations URL: https://doi.org/10.1016/j.ipl.2015.09.006 https://hal-univ-bourgogne.archives-ouvertes.fr/hal-01418254 BASE Hide details 2 Avoiding vincular patterns on alternating words Gao, Alice L.L.; Kitaev, Sergey; Zhang, Philip B.. - 2016 BASE Show details 3 Mahonian STAT on words Kitaev, Sergey; Vajnovszki, Vincent. - 2016 BASE Show details 4 Word problem of the Perkins semigroup via directed acyclic graphs Kitaev, Sergey; Seif, Steven. - 2008 BASE Show details

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