Kitaev, Sergey (2003) Generalized pattern avoidance with additional restrictions. Séminaire Lotharingien de Combinatoire, 48. ISSN 1286-4889Full text not available in this repository. (Request a copy from the Strathclyde author)
Babson and Steingrímsson introduced generalized permutation patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. We consider n-permutations that avoid the generalized pattern 1-32 and whose k rightmost letters form an increasing subword. The number of such permutations is a linear combination of Bell numbers. We find a bijection between these permutations and all partitions of an (n-1)-element set with one subset marked that satisfy certain additional conditions. Also we find the e.g.f. for the number of permutations that avoid a generalized 3-pattern with no dashes and whose k leftmost or k rightmost letters form either an increasing or decreasing subword. Moreover, we find a bijection between n-permutations that avoid the pattern 132 and begin with the pattern 12 and increasing rooted trimmed trees with n+1 nodes.
|Keywords:||Electronic computers. Computer science, Computational Theory and Mathematics|
|Subjects:||Science > Mathematics > Electronic computers. Computer science|
|Department:||Faculty of Science > Computer and Information Sciences|
|Depositing user:||Pure Administrator|
|Date Deposited:||12 Sep 2014 14:29|
|Last modified:||05 Mar 2017 01:07|