Compositions inside a rectangle and unimodality
| dc.creator | Sagan, Bruce E. | |
| dc.date | 2007-07-06 | |
| dc.date.accessioned | 2026-07-07T08:14:30Z | |
| dc.date.available | 2026-07-07T08:14:30Z | |
| dc.description | Let c^{k,l}(n) be the number of compositions (ordered partitions) of the integer n whose Ferrers diagram fits inside a k-by-l rectangle. The purpose of this note is to give a simple, algebraic proof of a conjecture of Vatter that the sequence c^{k,l}(0), c^{k,l}(1), ..., c^{k,l}(kl) is unimodal. The problem of giving a combinatorial proof of this fact is discussed, but is still open. | |
| dc.description | 9 pages, 1 figure, see related papers at http://www.math.msu.edu/~sagan | |
| dc.identifier | https://arxiv.org/abs/0707.1052 | |
| dc.identifier | http://arxiv.org/abs/0707.1052 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/133143 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A17; 05A20 | |
| dc.title | Compositions inside a rectangle and unimodality | |
| dc.type | text |