A polynomial generalization of the power-compositions determinant
| dc.creator | Brunat, Josep M. | |
| dc.creator | Montes, Antonio | |
| dc.date | 2006-01-31 | |
| dc.date.accessioned | 2026-07-07T06:59:31Z | |
| dc.date.available | 2026-07-07T06:59:31Z | |
| dc.description | Let $C(n,p)$ be the set of $p$-compositions of an integer $n$, i.e., the set of $p$-tuples $\bmα=(α_1,...,α_p)$ of nonnegative integers such that $α_1+...+α_p=n$, and $\mathbf{x}=(x_1,...,x_p)$ a vector of indeterminates. For $\bmα$ and ${\bmβ}$ two $p$-compositions of $n$, define $(\mathbf{x}+\bmα)^{\bmβ} = (x_1+α_1)^{β_1}... x_p+α_p)^{β_p}$. In this paper we prove an explicit formula for the determinant $\det_{\bmα,{\bmβ}\in C(n,p)}((\mathbf{x}+\bmα)^{\bmβ})$. In the case $x_1=...=x_p$ the formula gives a proof of a conjecture by C.~Krattenthaler. | |
| dc.description | 11 pages, see also http://www-ma2.upc.edu/~montes/ | |
| dc.identifier | https://arxiv.org/abs/math/0601756 | |
| dc.identifier | http://arxiv.org/abs/math/0601756 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/107776 | |
| dc.subject | Combinatorics | |
| dc.subject | 11C20; 15A36; 05A10; 05A19 | |
| dc.title | A polynomial generalization of the power-compositions determinant | |
| dc.type | text |