Enumeration of 3-letter patterns in compositions
| dc.creator | Heubach, S. | |
| dc.creator | Mansour, T. | |
| dc.date | 2006-03-13 | |
| dc.date.accessioned | 2026-07-07T07:06:48Z | |
| dc.date.available | 2026-07-07T07:06:48Z | |
| dc.description | Let A be any set of positive integers and n a positive integer. A composition of n with parts in A is an ordered collection of one or more elements in A whose sum is n. We derive generating functions for the number of compositions of n with m parts in A that have r occurrences of 3-letter patterns formed by two (adjacent) instances of levels, rises and drops. We also derive asymptotics for the number of compositions of n that avoid a given pattern. Finally, we obtain the generating function for the number of k-ary words of length m which contain a prescribed number of occurrences of a given pattern as a special case of our results. | |
| dc.description | 20 pages, 1 figure; accepted for the Proceedings of the 2005 Integer Conference | |
| dc.identifier | https://arxiv.org/abs/math/0603285 | |
| dc.identifier | http://arxiv.org/abs/math/0603285 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/110160 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A05 (primary), 05A15, 05A16 (secondary) | |
| dc.title | Enumeration of 3-letter patterns in compositions | |
| dc.type | text |