Noncrossing partitions under rotation and reflection
| dc.creator | Callan, David | |
| dc.creator | Smiley, Len | |
| dc.date | 2005-10-20 | |
| dc.date | 2005-10-30 | |
| dc.date.accessioned | 2026-07-07T06:47:44Z | |
| dc.date.available | 2026-07-07T06:47:44Z | |
| dc.description | We consider noncrossing partitions of [n] under the action of (i) the reflection group (of order 2), (ii) the rotation group (cyclic of order n) and (iii) the rotation/reflection group (dihedral of order 2n). First, we exhibit a bijection from rotation classes to bicolored plane trees on n edges, and consider its implications. Then we count noncrossing partitions of [n] invariant under reflection and show that, somewhat surprisingly, they are equinumerous with rotation classes invariant under reflection. The proof uses a pretty involution originating in work of Germain Kreweras. We conjecture that the "equinumerous" result also holds for arbitrary partitions of [n]. | |
| dc.description | 15 pages, LaTeX, PSTricks, .eps figures | |
| dc.identifier | https://arxiv.org/abs/math/0510447 | |
| dc.identifier | http://arxiv.org/abs/math/0510447 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/103753 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A15 | |
| dc.title | Noncrossing partitions under rotation and reflection | |
| dc.type | text |