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 a sequence of transpositions of adjacent commuting 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 systems of non-linear q-equations for the associated generating functions. Here, we show that an alternative recursive description leads to explicit expressions for these generating functions. (C) 2018 Elsevier Inc. All rights reserved.

Biagioli R, Bousquet-Melou M, Jouhet F, Nadeau P (2018). Length enumeration of fully commutative elements in finite and affine Coxeter groups. JOURNAL OF ALGEBRA, 513, 466-515 [10.1016/j.jalgebra.2018.06.009].

Length enumeration of fully commutative elements in finite and affine Coxeter groups

Biagioli R;
2018

Abstract

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 a sequence of transpositions of adjacent commuting 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 systems of non-linear q-equations for the associated generating functions. Here, we show that an alternative recursive description leads to explicit expressions for these generating functions. (C) 2018 Elsevier Inc. All rights reserved.
2018
Biagioli R, Bousquet-Melou M, Jouhet F, Nadeau P (2018). Length enumeration of fully commutative elements in finite and affine Coxeter groups. JOURNAL OF ALGEBRA, 513, 466-515 [10.1016/j.jalgebra.2018.06.009].
Biagioli R; Bousquet-Melou M; Jouhet F; Nadeau P
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/802577
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