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Distributive coset graphs of finite Coxeter groups. (English) Zbl 1062.20045
Summary: Let \(W\) be a finite Coxeter group, \(W_J\) a parabolic subgroup of \(W\) and \(X_J\) the set of distinguished coset representatives of \(W_J\) in \(W\) equipped with the induced weak Bruhat ordering of \(W\). All instances when \(X_J\) is a distributive lattice are known. In this note we present a short conceptual proof of this result.
MSC:
20F55 Reflection and Coxeter groups (group-theoretic aspects)
05E15 Combinatorial aspects of groups and algebras (MSC2010)
06A07 Combinatorics of partially ordered sets
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