1. Poset edge densities, nearly reduced words, and barely set-valued tableaux
- Author
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Alexander Yong, Victor Reiner, and Bridget Eileen Tenner
- Subjects
0102 computer and information sciences ,01 natural sciences ,Coincidence ,Theoretical Computer Science ,Combinatorics ,symbols.namesake ,Lattice (order) ,FOS: Mathematics ,Discrete Mathematics and Combinatorics ,Mathematics - Combinatorics ,0101 mathematics ,Mathematics::Representation Theory ,Mathematics ,Mathematics::Combinatorics ,010102 general mathematics ,Coxeter group ,Cartesian product ,16. Peace & justice ,Bruhat order ,Weighting ,05A99, 05E10 ,Computational Theory and Mathematics ,010201 computation theory & mathematics ,symbols ,Combinatorics (math.CO) ,Partially ordered set - Abstract
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., Comment: to appear in Journal of Combinatorial Theory, Series A
- Published
- 2016
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