A combinatorial interpretation of the eigensequence for composition
| dc.creator | Callan, David | |
| dc.date | 2005-07-08 | |
| dc.date | 2005-07-20 | |
| dc.date.accessioned | 2026-07-07T05:21:32Z | |
| dc.date.available | 2026-07-07T05:21:32Z | |
| dc.description | The monic sequence that shifts left under convolution with itself is the Catalan numbers with 130+ combinatorial interpretations. Here we establish a combinatorial interpretation for the monic sequence that shifts left under composition: it counts permutations that contain a 3241 pattern only as part of a 35241 pattern. We give two recurrences, the first allowing relatively fast computation, the second similar to one for the Catalan numbers. Among the 4 times 4! = 96 similarly restricted patterns involving 4 letters (such as 4\underline{2}31: a 431 pattern only occurs as part of a 4231), four different counting sequences arise: 64 give the Catalan numbers, 16 give the Bell numbers, 12 give sequence A051295 in OEIS, and 4 give a new sequence with an explicit formula. | |
| dc.description | minor corrections and improvements | |
| dc.identifier | https://arxiv.org/abs/math/0507169 | |
| dc.identifier | http://arxiv.org/abs/math/0507169 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75723 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A15 | |
| dc.title | A combinatorial interpretation of the eigensequence for composition | |
| dc.type | text |