Sets, Lists and Noncrossing Partitions
| dc.creator | Callan, David | |
| dc.date | 2007-11-29 | |
| dc.date | 2008-02-07 | |
| dc.date.accessioned | 2026-07-07T09:18:56Z | |
| dc.date.available | 2026-07-07T09:18:56Z | |
| dc.description | Partitions of [n]={1,2,...,n} into sets of lists are counted by sequence number A000262 in the On-Line Encyclopedia of Integer Sequences. They are somewhat less numerous than partitions of [n] into lists of sets, A000670. Here we observe that the former are actually equinumerous with partitions of [n] into lists of *noncrossing* sets and give a bijective proof. We show that partitions of [n] into sets of noncrossing lists are counted by A088368 and generalize this result to introduce a transform on integer sequences that we dub the "noncrossing partition" transform. We also derive recurrence relations to count partitions of [n] into lists of noncrossing lists. | |
| dc.description | 8 pages, published version includes revisions | |
| dc.identifier | https://arxiv.org/abs/0711.4841 | |
| dc.identifier | http://arxiv.org/abs/0711.4841 | |
| dc.identifier | Journal of Integer Sequences, Vol. 11, 2008, Article 08.1.3 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/154210 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A15 | |
| dc.title | Sets, Lists and Noncrossing Partitions | |
| dc.type | text |