k-noncrossing and k-nonnesting graphs and fillings of Ferrers diagrams
| dc.creator | de Mier, Anna | |
| dc.date | 2006-02-09 | |
| dc.date | 2006-04-09 | |
| dc.date.accessioned | 2026-07-07T07:03:16Z | |
| dc.date.available | 2026-07-07T07:03:16Z | |
| dc.description | We give a correspondence between graphs with a given degree sequence and fillings of Ferrers diagrams by nonnegative integers with prescribed row and column sums. In this setting, k-crossings and k-nestings of the graph become occurrences of the identity and the antiidentity matrices in the filling. We use this to show the equality of the numbers of k-noncrossing and k-nonnesting graphs with a given degree sequence. This generalizes the analogous result for matchings and partition graphs of Chen, Deng, Du, Stanley, and Yan, and extends results of Klazar to k>2. Moreover, this correspondence reinforces the links recently discovered by Krattenthaler between fillings of diagrams and the results of Chen et al. | |
| dc.description | 19 pages, 3 figures, section 3 expanded, added references | |
| dc.identifier | https://arxiv.org/abs/math/0602195 | |
| dc.identifier | http://arxiv.org/abs/math/0602195 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/108909 | |
| dc.subject | Combinatorics | |
| dc.title | k-noncrossing and k-nonnesting graphs and fillings of Ferrers diagrams | |
| dc.type | text |