Bruhat order on classical Weyl groups: minimal chains and covering relation

Authors:
Federico Incitti
Affiliations:
Department of Mathematics, University of Linköping, 58183 Linköping, Sweden
Venue:
European Journal of Combinatorics
Year:
2005

Citing 2
Cited 1

Enumerative combinatorics

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The Bruhat order on the involutions of the hyperoctahedral group

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Journal of Combinatorial Theory Series A

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Abstract

In this paper we study some aspects of the Bruhat order on classical Weyl groups, obtaining a direct combinatorial description of the minimal chains, that is chains with the lexicographically minimal labelling. Moreover, we find a combinatorial characterization of the covering relation in the hyperoctahedral group and in the even-signed permutation group, providing results analogous to the well-known characterization of the covering relation in the symmetric group.