Classifying Descents According to equivalence mod k
| dc.creator | Kitaev, Sergey | |
| dc.creator | Remmel, Jeffrey | |
| dc.date | 2006-04-20 | |
| dc.date.accessioned | 2026-07-07T07:11:09Z | |
| dc.date.available | 2026-07-07T07:11:09Z | |
| dc.description | In [S. Kitaev and J. Remmel: Classifying descents according to parity] the authors refine the well-known permutation statistic "descent" by fixing parity of (exactly) one of the descent's numbers. In this paper, we generalize the results of [S. Kitaev and J. Remmel: Classifying descents according to parity] by studying descents according to whether the first or the second element in a descent pair is equivalent to $k$ mod $k\geq 2$. We provide either an explicit or an inclusion-exclusion type formula for the distribution of the new statistics. Based on our results we obtain combinatorial proofs of a number of remarkable identities. We also provide bijective proofs of some of our results and state a number of open problems. | |
| dc.description | 42 pages | |
| dc.identifier | https://arxiv.org/abs/math/0604455 | |
| dc.identifier | http://arxiv.org/abs/math/0604455 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/111645 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A15, 05E05 | |
| dc.title | Classifying Descents According to equivalence mod k | |
| dc.type | text |