Monomial bases related to the n! conjecture
| dc.creator | Aval, Jean-Christophe | |
| dc.date | 2007-11-06 | |
| dc.date.accessioned | 2026-07-07T08:41:01Z | |
| dc.date.available | 2026-07-07T08:41:01Z | |
| dc.description | The purpose of this paper is to find a new way to prove the $n!$ conjecture for particular partitions. The idea is to construct a monomial and explicit basis for the space $M_μ$. We succeed completely for hook-shaped partitions, i.e., $μ=(K+1,1^L)$. We are able to exhibit a basis and to verify that its cardinality is indeed $n!$, that it is linearly independent and that it spans $M_μ$. We derive from this study an explicit and simple basis for $I_μ$, the annihilator ideal of $Δ_μ$. This method is also successful for giving directly a basis for the homogeneous subspace of $M_μ$ consisting of elements of 0 $x$-degree. | |
| dc.identifier | https://arxiv.org/abs/0711.0898 | |
| dc.identifier | http://arxiv.org/abs/0711.0898 | |
| dc.identifier | Discrete Mathematics 224 (2000) 15-35 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/141550 | |
| dc.subject | Combinatorics | |
| dc.title | Monomial bases related to the n! conjecture | |
| dc.type | text |