Some Enumerations for Parking Functions
| dc.creator | Huang, Po-Yi | |
| dc.creator | Ma, Jun | |
| dc.creator | Yeh, Jean | |
| dc.date | 2008-06-03 | |
| dc.date.accessioned | 2026-07-07T09:42:22Z | |
| dc.date.available | 2026-07-07T09:42:22Z | |
| dc.description | In this paper, let $\mathcal{P}_{n,n+k;\leq n+k}$ (resp. $\mathcal{P}_{n;\leq s}$) denote the set of parking functions $α=(a_1,...,a_n)$ of length $n$ with $n+k$ (respe. $n$)parking spaces satisfying $1\leq a_i\leq n+k$ (resp. $1\leq a_i\leq s$) for all $i$. Let $p_{n,n+k;\leq n+k}=|\mathcal{P}_{n,n+k;\leq n+k}|$ and $p_{n;\leq s}=|\mathcal{P}_{n;\leq s}|$. Let $\mathcal{P}_{n;\leq s}^l$ denote the set of parking functions $α=(a_1,...,a_n)\in\mathcal{P}_{n;\leq s}$ such that $a_1=l$ and $p_{n;\leq s}^l=|\mathcal{P}_{n;\leq s}^l|$. We derive some formulas and recurrence relations for the sequences $p_{n,n+k;\leq n+k}$, $p_{n;\leq s}$ and $p_{n;\leq s}^l$ and give the generating functions for these sequences. We also study the asymptotic behavior for these sequences. | |
| dc.identifier | https://arxiv.org/abs/0806.0424 | |
| dc.identifier | http://arxiv.org/abs/0806.0424 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/162158 | |
| dc.subject | Combinatorics | |
| dc.title | Some Enumerations for Parking Functions | |
| dc.type | text |