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| HAL: hal-00012121, version 1 |
| arXiv: math.CO/0202071 |
| Detailed view |  Export this paper |
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| Advances in Mathematics 181,No.2 (2004) 353-367 |
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| Ideals of Quasi-Symmetric Functions and Super-Covariant Polynomials for S_n |
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| J. -C. Aval 1F. Bergeron |
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| (2002) |
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| 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. |
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| 1: | Théorie des Nombres et Algorithmique Arithmétique (A2X) |
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CNRS : UMR5465 – Université Sciences et Technologies - Bordeaux I |
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| Subject | : | Mathematics/Combinatorics |
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| Fulltext link: |
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| http://fr.arXiv.org/abs/math.CO/0202071 |
| hal-00012121, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00012121 | |
| oai:hal.archives-ouvertes.fr:hal-00012121 | |
| From: Import arXiv | |
| Submitted on: Sunday, 16 October 2005 16:40:37 | |
| Updated on: Sunday, 16 October 2005 16:40:37 | |
