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.
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.
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Jean Fromentin 1
@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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