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Main Authors: Biagioli, Riccardo, Bousquet-Mélou, Mireille, Jouhet, Frédéric, Nadeau, Philippe
Format: Preprint
Published: 2016
Subjects:
Online Access:https://arxiv.org/abs/1612.07591
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author Biagioli, Riccardo
Bousquet-Mélou, Mireille
Jouhet, Frédéric
Nadeau, Philippe
author_facet Biagioli, Riccardo
Bousquet-Mélou, Mireille
Jouhet, Frédéric
Nadeau, Philippe
contents An element w of a Coxeter group W is said to be fully commutative, if any reduced expression of w can be obtained from any other by transposing adjacent pairs of generators. These elements were described in 1996 by Stembridge in the case of finite irreducible groups, and more recently by Biagioli, Jouhet and Nadeau (BJN) in the affine cases. We focus here on the length enumeration of these elements. Using a recursive description, BJN established for the associated generating functions systems of non-linear q-equations. Here, we show that an alternative recursive description leads to explicit expressions for these generating functions.
format Preprint
id arxiv_https___arxiv_org_abs_1612_07591
institution arXiv
publishDate 2016
record_format arxiv
spellingShingle Length enumeration of fully commutative elements in finite and affine Coxeter groups
Biagioli, Riccardo
Bousquet-Mélou, Mireille
Jouhet, Frédéric
Nadeau, Philippe
Combinatorics
An element w of a Coxeter group W is said to be fully commutative, if any reduced expression of w can be obtained from any other by transposing adjacent pairs of generators. These elements were described in 1996 by Stembridge in the case of finite irreducible groups, and more recently by Biagioli, Jouhet and Nadeau (BJN) in the affine cases. We focus here on the length enumeration of these elements. Using a recursive description, BJN established for the associated generating functions systems of non-linear q-equations. Here, we show that an alternative recursive description leads to explicit expressions for these generating functions.
title Length enumeration of fully commutative elements in finite and affine Coxeter groups
topic Combinatorics
url https://arxiv.org/abs/1612.07591