The Bruhat order on the involutions of the hyperoctahedral group.
type: Item
instance of: scholarly article
title: The Bruhat order on the involutions of the hyperoctahedral group.
zbMATH Open document ID: 1056.20027
DOI: 10.1016/S0195-6698(03)00103-3
author: Federico Incitti
published in: European Journal of Combinatorics
publication date: 2003-11-16T00:00:00Z
review text: The subject of Coxeter groups and their posets using the Bruhat ordering became an active area of research. Several generalizations were made to the Bruhat order defined on a Coxeter group. Schubert polynomials and their multiplication can be defined right from such posets. This article is a serious attempt to apply a lot of well known results to a specific group, namely the hyperoctahedral group \(B_n\). It is a profound contribution to the subject to show that the graph of the involutions of \(B_n\) is graded, EL-shellable, Cohen-Macaulay, Eulerian and Gorenstein. The author has written the article neatly and explained every single concept that is needed in the sequel. However this article is mostly computational oriented rather than theoretic, although it opens the road to more sophisticated studies in the area.
reviewed by: A. Aljouiee
Mathematics Subject Classification ID: 20F55
Mathematics Subject Classification ID: 20C30
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 06A07
Mathematics Subject Classification ID: 05E15
Mathematics Subject Classification ID: 05E25
zbMATH DE Number: 2003949
zbMATH Keywords: graphs of involutions
zbMATH Keywords: hyperoctahedral groups
zbMATH Keywords: Bruhat orders
zbMATH Keywords: graded posets
zbMATH Keywords: rank functions
zbMATH Keywords: EL-shellable posets
zbMATH Keywords: Cohen-Macaulay posets
zbMATH Keywords: Eulerian posets
zbMATH Keywords: Coxeter groups
zbMATH Keywords: Schubert polynomials
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2003949