Block number, descents and Schur positivity of fully commutative elements in Bn

Eli Bagno; Riccardo Biagioli; Frédéric Jouhet; Yuval Roichman

doi:10.1016/j.ejc.2021.103464

Block number, descents and Schur positivity of fully commutative elements in B_n

Eli Bagno, Riccardo Biagioli, Frédéric Jouhet, Yuval Roichman

Department of Mathematics

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

Abstract

The distribution of Coxeter descents and block number over the set of fully commutative elements in the hyperoctahedral group B_n, FC(B_n), is studied in this paper. We prove that the associated Chow quasi-symmetric generating function is equal to a non-negative sum of products of two Schur functions. The proof involves a decomposition of FC(B_n) into a disjoint union of two-sided Barbash–Vogan combinatorial cells, a type B extension of Rubey's descent preserving involution on 321-avoiding permutations and a detailed study of the intersection of FC(B_n) with S_n-cosets which yields a new decomposition of FC(B_n) into disjoint subsets called fibers. We also compare two different type B Schur-positivity notions, arising from works of Chow and Poirier.

Original language	English
Article number	103464
Journal	European Journal of Combinatorics
Volume	101
DOIs	https://doi.org/10.1016/j.ejc.2021.103464
State	Published - Mar 2022

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics

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10.1016/j.ejc.2021.103464

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title = "Block number, descents and Schur positivity of fully commutative elements in Bn",

abstract = "The distribution of Coxeter descents and block number over the set of fully commutative elements in the hyperoctahedral group Bn, FC(Bn), is studied in this paper. We prove that the associated Chow quasi-symmetric generating function is equal to a non-negative sum of products of two Schur functions. The proof involves a decomposition of FC(Bn) into a disjoint union of two-sided Barbash–Vogan combinatorial cells, a type B extension of Rubey's descent preserving involution on 321-avoiding permutations and a detailed study of the intersection of FC(Bn) with Sn-cosets which yields a new decomposition of FC(Bn) into disjoint subsets called fibers. We also compare two different type B Schur-positivity notions, arising from works of Chow and Poirier.",

author = "Eli Bagno and Riccardo Biagioli and Fr{\'e}d{\'e}ric Jouhet and Yuval Roichman",

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doi = "10.1016/j.ejc.2021.103464",

language = "الإنجليزيّة",

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journal = "European Journal of Combinatorics",

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TY - JOUR

T1 - Block number, descents and Schur positivity of fully commutative elements in Bn

AU - Bagno, Eli

AU - Biagioli, Riccardo

AU - Jouhet, Frédéric

AU - Roichman, Yuval

PY - 2022/3

Y1 - 2022/3

N2 - The distribution of Coxeter descents and block number over the set of fully commutative elements in the hyperoctahedral group Bn, FC(Bn), is studied in this paper. We prove that the associated Chow quasi-symmetric generating function is equal to a non-negative sum of products of two Schur functions. The proof involves a decomposition of FC(Bn) into a disjoint union of two-sided Barbash–Vogan combinatorial cells, a type B extension of Rubey's descent preserving involution on 321-avoiding permutations and a detailed study of the intersection of FC(Bn) with Sn-cosets which yields a new decomposition of FC(Bn) into disjoint subsets called fibers. We also compare two different type B Schur-positivity notions, arising from works of Chow and Poirier.

AB - The distribution of Coxeter descents and block number over the set of fully commutative elements in the hyperoctahedral group Bn, FC(Bn), is studied in this paper. We prove that the associated Chow quasi-symmetric generating function is equal to a non-negative sum of products of two Schur functions. The proof involves a decomposition of FC(Bn) into a disjoint union of two-sided Barbash–Vogan combinatorial cells, a type B extension of Rubey's descent preserving involution on 321-avoiding permutations and a detailed study of the intersection of FC(Bn) with Sn-cosets which yields a new decomposition of FC(Bn) into disjoint subsets called fibers. We also compare two different type B Schur-positivity notions, arising from works of Chow and Poirier.

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DO - 10.1016/j.ejc.2021.103464

M3 - مقالة

SN - 0195-6698

VL - 101

JO - European Journal of Combinatorics

JF - European Journal of Combinatorics

M1 - 103464

ER -

Block number, descents and Schur positivity of fully commutative elements in B_n

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