Tamari lattices and noncrossing partitions in type B and beyond
| dc.creator | Thomas, Hugh | |
| dc.date | 2003-11-19 | |
| dc.date | 2005-01-29 | |
| dc.date.accessioned | 2026-07-07T05:03:03Z | |
| dc.date.available | 2026-07-07T05:03:03Z | |
| dc.description | The usual, or type A_n, Tamari lattice is a partial order on T_n^A, the triangulations of an (n+3)-gon. We define a partial order on T_n^B, the set of centrally symmetric triangulations of a (2n+2)-gon. We show that it is a lattice, and that it shares certain other nice properties of the A_n Tamari lattice, and therefore that it deserves to be considered the B_n Tamari lattice. We define a bijection between T_n^B and the non-crossing partitions of type B_n defined by Reiner. For S any subset of [n], Reiner defined a pseudo-type BD^S_n, to which is associated a subset of the noncrossing partitions of type B_n. We show that the elements of T^B_n which correspond to the noncrossing partitions of type BD^S_n posess a lattice structure induced from their inclusion in T^B_n. | |
| dc.description | 19 pages, 5 figures; version 2 replaces some incorrect lemmas and incorporates some other more minor improvements | |
| dc.identifier | https://arxiv.org/abs/math/0311334 | |
| dc.identifier | http://arxiv.org/abs/math/0311334 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69260 | |
| dc.subject | Combinatorics | |
| dc.subject | 05E15 | |
| dc.title | Tamari lattices and noncrossing partitions in type B and beyond | |
| dc.type | text |