Rook numbers and the normal ordering problem
| dc.creator | Varvak, Anna | |
| dc.date | 2004-02-23 | |
| dc.date | 2004-07-15 | |
| dc.date.accessioned | 2026-07-07T05:05:40Z | |
| dc.date.available | 2026-07-07T05:05:40Z | |
| dc.description | For an element $w$ in the Weyl algebra generated by $D$ and $U$ with relation $DU=UD+1$, the normally ordered form is $w=\sum c_{i,j}U^iD^j$. We demonstrate that the normal order coefficients $c_{i,j}$ of a word $w$ are rook numbers on a Ferrers board. We use this interpretation to give a new proof of the rook factorization theorem, which we use to provide an explicit formula for the coefficients $c_{i,j}$. We calculate the Weyl binomial coefficients: normal order coefficients of the element $(D+U)^n$ in the Weyl algebra. We extend all these results to the $q$-analogue of the Weyl algebra. We discuss further generalizations using $i$-rook numbers. | |
| dc.description | 14 pages, presented as poster in FPSAC'04 | |
| dc.identifier | https://arxiv.org/abs/math/0402376 | |
| dc.identifier | http://arxiv.org/abs/math/0402376 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70251 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A10 | |
| dc.title | Rook numbers and the normal ordering problem | |
| dc.type | text |