The sorting order on a Coxeter group

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

Let (W, S) be an arbitrary Coxeter system. For each word ω 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 subwords of ω. We show that the ω-sorting order is a supersolvable join-distributive lattice and that it is strictly between the weak and Bruhat orders on the group. Moreover, the ω-sorting order is a "maximal lattice" in the sense that the addition of any collection of Bruhat covers 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)
Pages (from-to)1285-1305
Number of pages21
JournalJournal of Combinatorial Theory, Series A
Volume116
Issue number8
DOIs
StatePublished - Nov 2009
Externally publishedYes

Fingerprint

Coxeter Group
Sorting
Distributive Lattice
Join
Antimatroid
Bruhat Order
Weak Order
Subword
Partial Order
Strictly
Generator
Cover
Arbitrary
Class

Keywords

  • Abstract convex geometry
  • Antimatroid
  • Catalan number
  • Coxeter group
  • Join-distributive lattice
  • Lattice
  • Partial order
  • Sorting algorithm
  • Supersolvable lattice

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science
  • Computational Theory and Mathematics

Cite this

The sorting order on a Coxeter group. / Armstrong, Drew.

In: Journal of Combinatorial Theory, Series A, Vol. 116, No. 8, 11.2009, p. 1285-1305.

Research output: Contribution to journalArticle

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