Poset edge densities, nearly reduced words, and barely set-valued tableaux

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:158

Article

Reiner, Victor¹  Tenner, Bridget Eileen²  Yong, Alexander³ 

[1] Univ Minnesota, Sch Math, Minneapolis, MN 55455 USA

[2] DePaul Univ, Dept Math Sci, Chicago, IL 60614 USA

[3] Univ Illinois, Dept Math, Urbana, IL 61801 USA

关键词: Reduced word;    0-Hecke;    NilHecke;    Monoid;    Grothendieck polynomial;    Tableau;    Dominant;    Rectangular shape;    Staircase shape;    Set-valued;   

DOI  :  10.1016/j.jcta.2018.03.010

来源: Elsevier

【 摘 要 】

In certain finite posets, the expected down-degree of their elements is the same whether computed with respect to either the uniform distribution or the distribution weighting an element by the number of maximal chains passing through it. We show that this coincidence of expectations holds for Cartesian products of chains, connected minuscule posets, weak Bruhat orders on finite Coxeter groups, certain lower intervals in Young's lattice, and certain lower intervals in the weak Bruhat order below dominant permutations. Our tools involve formulas for counting nearly reduced factorizations in 0-Hecke algebras; that is, factorizations that are one letter longer than the Coxeter group length. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free