Ideals of Quasi-Symmetric Functions and Super-Covariant Polynomials for S_n
| hal.structure.identifier | Théorie des Nombres et Algorithmique Arithmétique [A2X] | |
| dc.contributor.author | AVAL, J. -C. | |
| dc.contributor.author | BERGERON, F. | |
| dc.contributor.author | BERGERON, N. | |
| dc.date.created | 2002 | |
| dc.date.issued | 2004 | |
| dc.identifier.issn | 0001-8708 | |
| dc.description.abstractEn | The aim of this work is to study the quotient ring R_n of the ring Q[x_1,...,x_n] over the ideal J_n generated by non-constant homogeneous quasi-symmetric functions. We prove here that the dimension of R_n is given by C_n, the n-th Catalan number. This is also the dimension of the space SH_n of super-covariant polynomials, that is defined as the orthogonal complement of J_n with respect to a given scalar product. We construct a basis for R_n whose elements are naturally indexed by Dyck paths. This allows us to understand the Hilbert series of SH_n in terms of number of Dyck paths with a given number of factors. | |
| dc.language.iso | en | |
| dc.publisher | Elsevier | |
| dc.title.en | Ideals of Quasi-Symmetric Functions and Super-Covariant Polynomials for S_n | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Combinatoire [math.CO] | |
| dc.identifier.arxiv | math.CO/0202071 | |
| bordeaux.journal | Advances in Mathematics | |
| bordeaux.page | 353-367 | |
| bordeaux.volume | 181,No.2 | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00012121 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Non spécifiée | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00012121v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Advances%20in%20Mathematics&rft.date=2004&rft.volume=181,No.2&rft.spage=353-367&rft.epage=353-367&rft.eissn=0001-8708&rft.issn=0001-8708&rft.au=AVAL,%20J.%20-C.&BERGERON,%20F.&BERGERON,%20N.&rft.genre=article |
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