Affine permutations of type \(A\)
type: Item
instance of: scholarly article
title: Affine permutations of type \(A\)
zbMATH Open document ID: 0854.05002
author: Francesco Brenti
author: Anders Bjoerner
published in: The Electronic Journal of Combinatorics
publication date: 1996-07-21T00:00:00Z
full work available at URL: https://eudml.org/doc/118972
full work available at URL: R18
review text: Let \(\widetilde S_n\) denote the group (under composition) of all bijections \(\pi: \mathbb{Z}\to \mathbb{Z}\) such that \(\pi(x)+ n= \pi(x+ n)\) for all \(x\in \mathbb{Z}\), and \(\pi(1)+ \pi(2)+\cdots+ \pi(n)= (\begin{smallmatrix} n+ 1\\ 2\end{smallmatrix})\). This gives a realization of the affine Coxeter group \(\widetilde A_{n- 1}\). The authors study combinatorial properties of such affine permutations, such as the inversion table, weak order and Bruhat order.
reviewed by: E. J. F. Primrose
Mathematics Subject Classification ID: 05A05
Mathematics Subject Classification ID: 20F55
Mathematics Subject Classification ID: 06A07
zbMATH DE Number: 907657
zbMATH Keywords: Coxeter group
zbMATH Keywords: affine permutations
zbMATH Keywords: inversion table
zbMATH Keywords: weak order
zbMATH Keywords: Bruhat order
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 907657