Group Theory
A well-ordering of dual braid monoids
Comptes Rendus. Mathématique, Volume 346 (2008) no. 13-14, pp. 729-734.

Let Bn+ denote the dual braid monoid on n strands, i.e., the submonoid of the braid group Bn consisting of the braids that can be expressed as positive words in the Birman–Ko–Lee generators. We introduce a new normal form on Bn+, which is based on expressing every braid of Bn+ in terms of a certain finite sequence of braids of Bn1+. We deduce an inductive characterization of the Dehornoy ordering of dual braid monoids, and explicitly compute the associated order types.

Soit Bn+ le monoïde de tresses dual sur n brins, c'est-à-dire le sous-monoïde du groupe de tresses Bn formé par les tresses ayant une expression positive en les générateurs de Birman–Ko–Lee. Nous introduisons une nouvelle forme normale, dite cyclante, sur Bn+. Cette forme normale est basée sur une décomposition de chaque tresse de Bn+ en termes d'une suite de tresses de Bn1+. Nous en déduisons une caractérisation inductive de l'ordre de Dehornoy sur les monoïdes de tresses duaux, et calculons explicitement les types d'ordre associés.

Published online:
DOI: 10.1016/j.crma.2008.05.001
Fromentin, Jean 1

1 Laboratoire de mathématiques Nicolas-Oresme, UMR 6139 CNRS, Université de Caen BP 5186, 14032 Caen, France
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     title = {A well-ordering of dual braid monoids},
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Fromentin, Jean. A well-ordering of dual braid monoids. Comptes Rendus. Mathématique, Volume 346 (2008) no. 13-14, pp. 729-734. doi : 10.1016/j.crma.2008.05.001.

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