Plane partitions I: a generalization of MacMahon's formula
| dc.creator | Ciucu, Mihai | |
| dc.date | 1998-08-04 | |
| dc.date | 2004-10-29 | |
| dc.date.accessioned | 2026-07-07T05:25:37Z | |
| dc.date.available | 2026-07-07T05:25:37Z | |
| dc.description | The number of plane partitions contained in a given box was shown by MacMahon to be given by a simple product formula. By a simple bijection, this formula also enumerates lozenge tilings of hexagons of side-lengths $a,b,c,a,b,c$ (in cyclic order) and angles of 120 degrees. We present a generalization in the case $b=c$ by giving simple product formulas enumerating lozenge tilings of regions obtained from a hexagon of side-lengths $a,b+k,b,a+k,b,b+k$ (where $k$ is an arbitrary non-negative integer) and angles of 120 degrees by removing certain triangular regions along its symmetry axis. | |
| dc.description | 35 pages, 34 figures. New to this version: a few typos were corrected, and the journal information is included. Memoirs of Amer. Math. Soc., accepted, to appear | |
| dc.identifier | https://arxiv.org/abs/math/9808017 | |
| dc.identifier | http://arxiv.org/abs/math/9808017 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77246 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A15, 05B45 | |
| dc.title | Plane partitions I: a generalization of MacMahon's formula | |
| dc.type | text |