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Garside families in Artin–Tits monoids and low elements in Coxeter groups

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Academic year: 2021

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Table 1 and Proposition 5.1 below give some information about the smallest Garside family in a few Artin-Tits monoids
Table 1. The smallest Garside family F in the Artin–Tits monoid associated with the Coxeter system (W, S); when F is finite, it must consist of all right-divisors of the elements of some minimal finite set E (the “extremal elements”).

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