Labeled Partitions with Colored Permutations
| dc.creator | Chen, William Y. C. | |
| dc.creator | Gao, Henry Y. | |
| dc.creator | He, Jia | |
| dc.date | 2008-10-19 | |
| dc.date.accessioned | 2026-07-07T10:11:36Z | |
| dc.date.available | 2026-07-07T10:11:36Z | |
| dc.description | In this paper, we extend the notion of labeled partitions with ordinary permutations to colored permutations in the sense that the colors are endowed with a cyclic structure. We use labeled partitions with colored permutations to derive the generating function of the $\mathrm{fmaj}_k$ indices of colored permutations. The second result is a combinatorial treatment of a relation on the q-derangement numbers with respect to colored permutations which leads to the formula of Chow for signed permutations and the formula of Faliharimalala and Zeng [10] on colored permutations. The third result is an involution on permutations that implies the generating function formula for the signed q-counting of the major indices due to Gessel and Simon. This involution can be extended to signed permutations. In this way, we obtain a combinatorial interpretation of a formula of Adin, Gessel and Roichman. | |
| dc.description | 14 pages | |
| dc.identifier | https://arxiv.org/abs/0810.3388 | |
| dc.identifier | http://arxiv.org/abs/0810.3388 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/171910 | |
| dc.subject | Combinatorics | |
| dc.title | Labeled Partitions with Colored Permutations | |
| dc.type | text |