On lexicographic semi-commutations

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Abstract

We give a characterization of the commutation graphs for which there exists a complete semi-commutation system. From which, we deduce a characterization of semi-commutation systems for which the set of minimal words and the set of irreducible words are equal.

Résumé

Dans cette article, nous caractérisons les graphes de commutation pour lesquels il existe un système de semi-commutation complet. Nous en déduisons une caractérisation des systèmes de semi-commutation pour lesquels l'ensemble des mots irréductibles est égal à l'ensemble des mots minimaux.

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