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hal.structure.identifierLaboratoire Bordelais de Recherche en Informatique [LaBRI]
hal.structure.identifierThéorie des Nombres et Algorithmique Arithmétique [A2X]
dc.contributor.authorAVAL, Jean-Christophe
hal.structure.identifierDepartment of Mathematics and Statistics [Toronto]
dc.contributor.authorBERGERON, Nantel
dc.date.created2001-09-20
dc.date.issued2003
dc.identifier.issn0002-9939
dc.description.abstractEnWe 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.isoen
dc.publisherAmerican Mathematical Society
dc.title.enCatalan paths, Quasi-symmetric functions and Super-Harmonic Spaces
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Combinatoire [math.CO]
dc.subject.halMathématiques [math]/Algèbre commutative [math.AC]
dc.subject.halMathématiques [math]/Anneaux et algèbres [math.RA]
dc.identifier.arxivmath/0109147
bordeaux.journalProceedings of the American Mathematical Society
bordeaux.page1053-1062
bordeaux.volume131
bordeaux.peerReviewedoui
hal.identifierhal-00185470
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00185470v1
bordeaux.COinSctx_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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