Geodesic
Growth function for a class of monoids
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009) (2009).

Voir la notice de l'article provenant de la source Episciences

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. 
@article{DMTCS_2009_special_256_a50,
     author = {Albenque, Marie and Nadeau, Philippe},
     title = {Growth function for a class of monoids},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)},
     year = {2009},
     doi = {10.46298/dmtcs.2728},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2728/}
}
TY  - JOUR
AU  - Albenque, Marie
AU  - Nadeau, Philippe
TI  - Growth function for a class of monoids
JO  - Discrete mathematics & theoretical computer science
PY  - 2009
VL  - DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2728/
DO  - 10.46298/dmtcs.2728
LA  - en
ID  - DMTCS_2009_special_256_a50
ER  - 
%0 Journal Article
%A Albenque, Marie
%A Nadeau, Philippe
%T Growth function for a class of monoids
%J Discrete mathematics & theoretical computer science
%D 2009
%V DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2728/
%R 10.46298/dmtcs.2728
%G en
%F DMTCS_2009_special_256_a50
Albenque, Marie; Nadeau, Philippe. Growth function for a class of monoids. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009) (2009). doi : 10.46298/dmtcs.2728. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2728/

Cité par Sources :