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

Victor Reiner, Bridget Eileen Tenner, Alexander Yong

Research output: Contribution to journalArticle

6 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)66-125
Number of pages60
JournalJournal of Combinatorial Theory. Series A
Volume158
DOIs
StatePublished - Aug 2018

Keywords

  • 0-Hecke
  • Dominant
  • Grothendieck polynomial
  • Monoid
  • NilHecke
  • Rectangular shape
  • Reduced word
  • Set-valued
  • Staircase shape
  • Tableau

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