![]() |
Discrete Mathematics & Theoretical Computer Science |
In this article we study a class of monoids that includes Garside monoids, and give a simple combinatorial proof of a formula for the formal sum of all elements of the monoid. This leads to a formula for the growth function of the monoid in the homogeneous case, and can also be lifted to a resolution of the monoid algebra. These results are then applied to known monoids related to Coxeter systems: we give the growth function of the Artin-Tits monoids, and do the same for the dual braid monoids. In this last case we show that the monoid algebras of the dual braid monoids of type A and B are Koszul algebras.
Source : ScholeXplorer
IsRelatedTo ARXIV 1603.04517 Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.1603.04517
|