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The order dimension of Bruhat order on infinite Coxeter groups. (English) Zbl 1067.20051

Summary: We give a quadratic lower bound and a cubic upper bound on the order dimension of the Bruhat (or strong) ordering of the affine Coxeter group \(\widetilde A_n\). We also demonstrate that the order dimension of the Bruhat order is infinite for a large class of Coxeter groups.

MSC:

20F55 Reflection and Coxeter groups (group-theoretic aspects)
06A07 Combinatorics of partially ordered sets
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