Finite automata and pattern avoidance in words
2005 (English)In: Journal of combinatorial theory. Series A (Print), ISSN 0097-3165, E-ISSN 1096-0899, Vol. 110, no 1, 127-145 p.Article in journal (Refereed) Published
We say that a word w on a totally ordered alphabet avoids the word v if there are no subsequences in w order-equivalent to v. In this paper we suggest a new approach to the enumeration of words on at most k letters avoiding a given pattern. By studying an automaton which for fixed k generates the words avoiding a given pattern we derive several previously known results for these kind of problems, as well as many new. In particular, we give a simple proof of the formula (Electron. J. Combin. 5(1998) #R15) for exact asymptotics for the number of words on k letters of length n that avoids the pattern 12...(l + 1). Moreover, we give the first combinatorial proof of the exact formula (Enumeration of words with forbidden patterns, Ph.D. Thesis, University of Pennsylvania, 1998) for the number of words on k letters of length n avoiding a three letter permutation pattern.
Place, publisher, year, edition, pages
2005. Vol. 110, no 1, 127-145 p.
IdentifiersURN: urn:nbn:se:kth:diva-78741DOI: 10.1016/j.jcta.2004.10.007ISI: 000228439100008OAI: oai:DiVA.org:kth-78741DiVA: diva2:492831
QC 201202272012-02-082012-02-082012-02-27Bibliographically approved