On $k$-noncrossing partitions
| dc.creator | Jin, Emma Y. | |
| dc.creator | Qin, Jing | |
| dc.creator | Reidys, Christian M. | |
| dc.date | 2007-10-26 | |
| dc.date | 2007-11-15 | |
| dc.date.accessioned | 2026-07-07T08:42:48Z | |
| dc.date.available | 2026-07-07T08:42:48Z | |
| dc.description | In this paper we prove a duality between $k$-noncrossing partitions over $[n]=\{1,...,n\}$ and $k$-noncrossing braids over $[n-1]$. This duality is derived directly via (generalized) vacillating tableaux which are in correspondence to tangled-diagrams \cite{Reidys:07vac}. We give a combinatorial interpretation of the bijection in terms of the contraction of arcs of tangled-diagrams. Furthermore it induces by restriction a bijection between $k$-noncrossing, 2-regular partitions over $[n]$ and $k$-noncrossing braids without isolated points over $[n-1]$. Since braids without isolated points correspond to enhanced partitions this allows, using the results of \cite{MIRXIN}, to enumerate 2-regular, 3-noncrossing partitions. | |
| dc.description | 5 pages; 3 figures | |
| dc.identifier | https://arxiv.org/abs/0710.5014 | |
| dc.identifier | http://arxiv.org/abs/0710.5014 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/142094 | |
| dc.subject | Combinatorics | |
| dc.subject | Representation Theory | |
| dc.subject | 06A07 | |
| dc.title | On $k$-noncrossing partitions | |
| dc.type | text |