The number of rhombus tilings of a "punctured" hexagon and the minor summation formula
| dc.creator | Okada, Soichi | |
| dc.creator | Krattenthaler, Christian | |
| dc.date | 1997-11-26 | |
| dc.date.accessioned | 2026-07-07T05:23:19Z | |
| dc.date.available | 2026-07-07T05:23:19Z | |
| dc.description | We compute the number of all rhombus tilings of a hexagon with sides $a,b+1,c,a+1,b,c+1$, of which the central triangle is removed, provided $a,b,c$ have the same parity. The result is a product of four numbers, each of which counts the number of plane partitions inside a given box. The proof uses nonintersecting lattice paths and a new identity for Schur functions, which is proved by means of the minor summation formula of Ishikawa and Wakayama. A symmetric generalization of this identity is stated as a conjecture. | |
| dc.description | 21 pages, AmS-TeX, uses TeXDraw | |
| dc.identifier | https://arxiv.org/abs/math/9712203 | |
| dc.identifier | http://arxiv.org/abs/math/9712203 | |
| dc.identifier | Adv. Appl. Math. 21 1998, 381-404 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76389 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A15 05A17 05A19 05B45 05E05 52C20 | |
| dc.title | The number of rhombus tilings of a "punctured" hexagon and the minor summation formula | |
| dc.type | text |