On certain spaces of lattice diagram polynomials
| dc.creator | Aval, Jean-Christophe | |
| dc.date | 2007-11-06 | |
| dc.date.accessioned | 2026-07-07T08:41:02Z | |
| dc.date.available | 2026-07-07T08:41:02Z | |
| dc.description | The aim of this work is to study some lattice diagram determinants $Δ_L(X,Y)$. We recall that $M_L$ denotes the space of all partial derivatives of $Δ_L$. 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.identifier | https://arxiv.org/abs/0711.0900 | |
| dc.identifier | http://arxiv.org/abs/0711.0900 | |
| dc.identifier | Discrete Mathematics 256 (2002) 557-575 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/141552 | |
| dc.subject | Combinatorics | |
| dc.title | On certain spaces of lattice diagram polynomials | |
| dc.type | text |