On certain spaces of lattice diagram polynomials
| hal.structure.identifier | Théorie des Nombres et Algorithmique Arithmétique [A2X] | |
| hal.structure.identifier | Laboratoire Bordelais de Recherche en Informatique [LaBRI] | |
| dc.contributor.author | AVAL, Jean-Christophe | |
| dc.date.created | 2001 | |
| dc.date.issued | 2002 | |
| dc.identifier.issn | 0012-365X | |
| dc.description.abstractEn | The aim of this work is to study some lattice diagram determinants $\Delta_L(X,Y)$. We recall that $M_L$ denotes the space of all partial derivatives of $\Delta_L$. In this paper, we want to study the space $M^k_{i,j}(X,Y)$ which is defined as the sum of $M_L$ spaces where the lattice diagrams $L$ are obtained by removing $k$ cells from a given partition, these cells being in the ``shadow'' of a given cell $(i,j)$ in a fixed Ferrers diagram. We obtain an upper bound for the dimension of the resulting space $M^k_{i,j}(X,Y)$, that we conjecture to be optimal. This dimension is a multiple of $n!$ and thus we obtain a generalization of the $n!$ conjecture. Moreover, these upper bounds associated to nice properties of some special symmetric differential operators (the ``shift'' operators) allow us to construct explicit bases in the case of one set of variables, i.e. for the subspace $M^k_{i,j}(X)$ consisting of elements of $0$ $Y$-degree. | |
| dc.language.iso | en | |
| dc.publisher | Elsevier | |
| dc.title.en | On certain spaces of lattice diagram polynomials | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Combinatoire [math.CO] | |
| dc.identifier.arxiv | 0711.0900 | |
| bordeaux.journal | Discrete Mathematics | |
| bordeaux.page | 557-575 | |
| bordeaux.volume | 256 | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00185525 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00185525v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Discrete%20Mathematics&rft.date=2002&rft.volume=256&rft.spage=557-575&rft.epage=557-575&rft.eissn=0012-365X&rft.issn=0012-365X&rft.au=AVAL,%20Jean-Christophe&rft.genre=article |
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