Growth function for a class of monoids

Marie Albenque; Philippe Nadeau

Growth function for a class of monoids

Marie Albenque
, Philippe Nadeau

Research output: Contribution to conference › Paper › peer-review

Abstract

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.

Original language	English
Pages	25-38
Number of pages	14
Publication status	Published - 1 Dec 2009
Externally published	Yes
Event	21st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'09 - Linz, Austria Duration: 20 Jul 2009 → 24 Jul 2009

Conference

Conference	21st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'09
Country/Territory	Austria
City	Linz
Period	20/07/09 → 24/07/09

Keywords

Garside group
Growth function
Koszul algebra
Monoid
Resolution

Cite this

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title = "Growth function for a class of monoids",

abstract = "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.",

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author = "Marie Albenque and Philippe Nadeau",

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AU - Albenque, Marie

AU - Nadeau, Philippe

PY - 2009/12/1

Y1 - 2009/12/1

N2 - 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.

AB - 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.

KW - Garside group

KW - Growth function

KW - Koszul algebra

KW - Monoid

KW - Resolution

UR - https://www.scopus.com/pages/publications/84860455180

M3 - Paper

AN - SCOPUS:84860455180

SP - 25

EP - 38

T2 - 21st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'09

Y2 - 20 July 2009 through 24 July 2009

ER -

Growth function for a class of monoids

Abstract

Conference

Keywords

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