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arXiv · 1112.0856

The absolute order of a permutation representation of a Coxeter group

Christos A. Athanasiadis·Yuval Roichman
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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.

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Christos A. Athanasiadis, Yuval Roichman. 2013-03-07. The absolute order of a permutation representation of a Coxeter group. https://arxiv.org/abs/1112.0856

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