AVAL, Jean-Christophe; BERGERON, Nantel

Métadonnées

Licence d’utilisation du document

AVAL, Jean-Christophe
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Théorie des Nombres et Algorithmique Arithmétique [A2X]

BERGERON, Nantel
Department of Mathematics and Statistics [Toronto]

Langue

Article de revue

Ce document a été publié dans

Proceedings of the American Mathematical Society. 2003, vol. 131, p. 1053-1062

American Mathematical Society

Résumé en anglais

We investigate the quotient ring $R$ of the ring of formal power series $\Q[[x_1,x_2,...]]$ over the closure of the ideal generated by non-constant quasi-\break symmetric functions. We show that a Hilbert basis of the quotient is naturally indexed by Catalan paths (infinite Dyck paths). We also give a filtration of ideals related to Catalan paths from $(0,0)$ and above the line $y=x-k$. We investigate as well the quotient ring $R_n$ of polynomial ring in $n$ variables over the ideal generated by non-constant quasi-symmetric polynomials. We show that the dimension of $R_n$ is bounded above by the $n$th Catalan number.< Réduire

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251