Vexillary elements in the hyperoctahedral group
type: Item
instance of: scholarly article
title: Vexillary elements in the hyperoctahedral group
zbMATH Open document ID: 0921.05060
DOI: 10.1023/A:1008633710118
author: Tao Kai Lam
author: Sara Billey
published in: Journal of Algebraic Combinatorics
publication date: 1999-09-29T00:00:00Z
review text: Vexillary permutations in the symmetric group are those permutations that avoid any subsequence with elements in the same relative position as 2143. The vexillary permutations have the property that any \(S_n\) Stanley symmetric function indexed by a vexillary permutation is actually a Schur function. The paper under review defines vexillary elements for the hyperoctahedral group as those for which the \(C_n\) Stanley symmetric function is actually a Schur \(Q\)-function. Taking this as a starting point, the authors then prove that vexillary elements in the hyperoctahedral group avoid any subsequence on a list of 18 separate patterns. This result was conjectured in \textit{T. K. Lam} [\(B_n\) Stanley symmetric functions, Discrete Math. 157, No. 1-3, 241-270 (1996; Zbl 0856.05095)].
Mathematics Subject Classification ID: 05E05
zbMATH DE Number: 1228565
zbMATH Keywords: vexillary permutations
zbMATH Keywords: Stanley symmetric function
zbMATH Keywords: Schur function
zbMATH Keywords: vexillary elements
zbMATH Keywords: hyperoctahedral group
reviewed by: Angèle. M. Hamel
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1228565