On cosets in Coxeter groups

Authors: SARAH B. HART, PETER J. ROWLEY

Abstract: In this paper the notion of Coxeter length for a subset of a Coxeter group, as introduced in [9], is investigated for various subsets of a Coxeter group. Mostly cosets of various subgroups are examined as well as the associated idea of X-posets, which is a vast generalization of the Bruhat order.

Keywords: Coxeter group, Bruhat order, cosets, partially ordered sets

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