[Bon ordre du monoïde de tresses dual]
Soit le monoïde de tresses dual sur n brins, c'est-à-dire le sous-monoïde du groupe de tresses formé par les tresses ayant une expression positive en les générateurs de Birman–Ko–Lee. Nous introduisons une nouvelle forme normale, dite cyclante, sur . Cette forme normale est basée sur une décomposition de chaque tresse de en termes d'une suite de tresses de . 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.
Let denote the dual braid monoid on n strands, i.e., the submonoid of the braid group consisting of the braids that can be expressed as positive words in the Birman–Ko–Lee generators. We introduce a new normal form on , which is based on expressing every braid of in terms of a certain finite sequence of braids of . We deduce an inductive characterization of the Dehornoy ordering of dual braid monoids, and explicitly compute the associated order types.
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@article{CRMATH_2008__346_13-14_729_0,
author = {Jean Fromentin},
title = {A well-ordering of dual braid monoids},
journal = {Comptes Rendus. Math\'ematique},
pages = {729--734},
publisher = {Elsevier},
volume = {346},
number = {13-14},
year = {2008},
doi = {10.1016/j.crma.2008.05.001},
language = {en},
}
Jean Fromentin. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.05.001/
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