Proper partitions of a polygon and k-Catalan numbers
| dc.creator | Sagan, Bruce | |
| dc.date | 2004-07-15 | |
| dc.date.accessioned | 2026-07-07T05:10:23Z | |
| dc.date.available | 2026-07-07T05:10:23Z | |
| dc.description | Let P be a polygon whose vertices have been colored (labeled) cyclically with the numbers 1,2,...,c. Motivated by conjectures of Propp, we are led to consider partitions of P into k-gons which are proper in the sense that each k-gon contains all c colors on its vertices. Counting the number of proper partitions involves a generalization of the k-Catalan numbers. We also show that in certain cases, any proper partition can be obtained from another by a sequence of moves called flips. | |
| dc.description | 16 pages, 2 figures, Latex, see related papers at http://www.math.msu.edu/~sagan | |
| dc.identifier | https://arxiv.org/abs/math/0407280 | |
| dc.identifier | http://arxiv.org/abs/math/0407280 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71911 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A10 (Primary) 05A05, 05A15, 05A19, 05C05 (Secondary) | |
| dc.title | Proper partitions of a polygon and k-Catalan numbers | |
| dc.type | text |