Circular Peaks and Hilbert Series
| dc.creator | Bouchard, Pierre | |
| dc.creator | Ma, Jun | |
| dc.creator | Yeh, Yeong-Nan | |
| dc.date | 2008-06-03 | |
| dc.date | 2008-06-05 | |
| dc.date.accessioned | 2026-07-07T09:42:35Z | |
| dc.date.available | 2026-07-07T09:42:35Z | |
| dc.description | The circular peak set of a permutation $σ$ is the set $\{σ(i)\mid σ(i-1)<σ(i)>σ(i+1)\}$. Let $\mathcal{P}_n$ be the set of all the subset $S\subseteq [n]$ such that there exists a permutation $σ$ which has the circular set $S$. We can make the set $\mathcal{P}_n$ into a poset $\mathscr{P}_n$ by defining $S\preceq T$ if $S\subseteq T$ as sets. In this paper, we prove that the poset $\mathscr{P}_n$ is a simplicial complex on the vertex set $[3,n]$. We study the $f$-vector, the $f$-polynomial, the reduced Euler characteristic, the M$\ddot{o}$bius function, the $h$-vector and the $h$-polynomial of $\mathscr{P}_n$. We also derive the zeta polynomial of $\mathscr{P}_n$ and give the formula for the number of the chains in $\mathscr{P}_n$. By the poset $\mathscr{P}_n$, we define two algebras $\mathcal{A}_{\mathscr{P}_n}$ and $\mathcal{B}_{\mathscr{P}_n}$. We consider the Hilbert polynomials and the Hilbert series of the algebra $\mathcal{A}_{\mathscr{P}_n}$ and $\mathcal{B}_{\mathscr{P}_n}$. | |
| dc.identifier | https://arxiv.org/abs/0806.0434 | |
| dc.identifier | http://arxiv.org/abs/0806.0434 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/162231 | |
| dc.subject | Combinatorics | |
| dc.title | Circular Peaks and Hilbert Series | |
| dc.type | text |