The sorting order on a Coxeter group

Research output: Contribution to conferencePaper

Abstract

Let (W,S) be an arbitrary Coxeter system. For each sequence ω = (ω 1, ω 2,. .) ∈ S* in the generators we define a partial order-called the ω-sorting order-on the set of group elements W ω ⊆ W that occur as finite subwords of !. We show that the ω-sorting order is a supersolvable join-distributive lattice and that it is strictly between the weak and strong Bruhat orders on the group. Moreover, the ω-sorting order is a "maximal lattice" in the sense that the addition of any collection of edges from the Bruhat order results in a nonlattice. Along the way we define a class of structures called supersolvable antimatroids and we show that these are equivalent to the class of supersolvable join-distributive lattices.

Original languageEnglish (US)
Pages411-416
Number of pages6
StatePublished - Dec 1 2008
Externally publishedYes
Event20th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'08 - Valparaiso, Chile
Duration: Jun 23 2008Jun 27 2008

Other

Other20th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'08
CountryChile
CityValparaiso
Period6/23/086/27/08

Keywords

  • Antimatroid
  • Convex geometry
  • Coxeter group
  • Join-distributive lattice
  • Supersolvable lattice

ASJC Scopus subject areas

  • Algebra and Number Theory

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  • Cite this

    Armstrong, D. (2008). The sorting order on a Coxeter group. 411-416. Paper presented at 20th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'08, Valparaiso, Chile.