The absolute order of a permutation representation of a Coxeter group

Abstract

A permutation representation of a Coxeter group $W$ naturally defines an absolute order. This family of partial orders (which includes the absolute order on $W$) is introduced and studied in this paper. Conditions under which the associated rank generating polynomial divides the rank generating polynomial of the absolute order on $W$ are investigated when $W$ is finite. Several examples, including a symmetric group action on perfect matchings, are discussed. As an application, a well-behaved absolute order on the alternating subgroup of $W$ is defined.

23 pages, 1 figure, revised version to be published in J. Algebraic Combinatorics

References in corpus (1)

• Generator Sets for the Alternating Group

Cited by in corpus (1)

• Kauffman's clock lattice as a graph of perfect matchings: a formula for its height