Enumerations of Permutations by Circular Descent Sets
| dc.creator | Chang, Hungyung | |
| dc.creator | Ma, Jun | |
| dc.creator | Yeh, Yeong-Nan | |
| dc.date | 2008-06-03 | |
| dc.date | 2008-06-05 | |
| dc.date.accessioned | 2026-07-07T09:42:34Z | |
| dc.date.available | 2026-07-07T09:42:34Z | |
| dc.description | The circular descent of a permutation $σ$ is a set $\{σ(i)\mid σ(i)>σ(i+1)\}$. In this paper, we focus on the enumerations of permutations by the circular descent set. Let $cdes_n(S)$ be the number of permutations of length $n$ which have the circular descent set $S$. We derive the explicit formula for $cdes_n(S)$. We describe a class of generating binary trees $T_k $ with weights. We find that the number of permutations in the set $CDES_n(S)$ corresponds to the weights of $T_k$. As a application of the main results in this paper, we also give the enumeration of permutation tableaux according to their shape. | |
| dc.identifier | https://arxiv.org/abs/0806.0433 | |
| dc.identifier | http://arxiv.org/abs/0806.0433 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/162230 | |
| dc.subject | Combinatorics | |
| dc.title | Enumerations of Permutations by Circular Descent Sets | |
| dc.type | text |