Catalan paths, Quasi-symmetric functions and Super-Harmonic Spaces
| hal.structure.identifier | Laboratoire Bordelais de Recherche en Informatique [LaBRI] | |
| hal.structure.identifier | Théorie des Nombres et Algorithmique Arithmétique [A2X] | |
| dc.contributor.author | AVAL, Jean-Christophe | |
| hal.structure.identifier | Department of Mathematics and Statistics [Toronto] | |
| dc.contributor.author | BERGERON, Nantel | |
| dc.date.created | 2001-09-20 | |
| dc.date.issued | 2003 | |
| dc.identifier.issn | 0002-9939 | |
| dc.description.abstractEn | 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. | |
| dc.language.iso | en | |
| dc.publisher | American Mathematical Society | |
| dc.title.en | Catalan paths, Quasi-symmetric functions and Super-Harmonic Spaces | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Combinatoire [math.CO] | |
| dc.subject.hal | Mathématiques [math]/Algèbre commutative [math.AC] | |
| dc.subject.hal | Mathématiques [math]/Anneaux et algèbres [math.RA] | |
| dc.identifier.arxiv | math/0109147 | |
| bordeaux.journal | Proceedings of the American Mathematical Society | |
| bordeaux.page | 1053-1062 | |
| bordeaux.volume | 131 | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00185470 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00185470v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Proceedings%20of%20the%20American%20Mathematical%20Society&rft.date=2003&rft.volume=131&rft.spage=1053-1062&rft.epage=1053-1062&rft.eissn=0002-9939&rft.issn=0002-9939&rft.au=AVAL,%20Jean-Christophe&BERGERON,%20Nantel&rft.genre=article |
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