Posets of annular non-crossing partitions of types B and D
| dc.creator | Nica, Alexandru | |
| dc.creator | Oancea, Ion | |
| dc.date | 2007-05-22 | |
| dc.date | 2008-02-12 | |
| dc.date.accessioned | 2026-07-07T09:19:41Z | |
| dc.date.available | 2026-07-07T09:19:41Z | |
| dc.description | We study the set $\sncb (p,q)$ of annular non-crossing permutations of type B, and we introduce a corresponding set $\ncb (p,q)$ of annular non-crossing partitions of type B, where $p$ and $q$ are two positive integers. We prove that the natural bijection between $\sncb (p,q)$ and $\ncb (p,q)$ is a poset isomorphism, where the partial order on $\sncb (p,q)$ is induced from the hyperoctahedral group $B_{p+q}$, while $\ncb (p,q)$ is partially ordered by reverse refinement. In the case when $q=1$, we prove that $\ncb (p,1)$ is a lattice with respect to reverse refinement order. We point out that an analogous development can be pursued in type D, where one gets a canonical isomorphism between $\sncd (p,q)$ and $\ncd (p,q)$. For $q=1$, the poset $\ncd (p,1)$ coincides with a poset ``$NC^{(D)} (p+1)$'' constructed in a paper by Athanasiadis and Reiner in 2004, and is a lattice by the results of that paper. | |
| dc.description | Revised version (shortened Introduction, corrected typos), 31 pages, 4 figures, to appear in Discrete Mathematics | |
| dc.identifier | https://arxiv.org/abs/0705.3076 | |
| dc.identifier | http://arxiv.org/abs/0705.3076 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/154483 | |
| dc.subject | Combinatorics | |
| dc.subject | 06A07 | |
| dc.title | Posets of annular non-crossing partitions of types B and D | |
| dc.type | text |