Marked mesh patterns in 132-avoiding permutations I

Details Marked mesh patterns in 132-avoiding permutations I Marked mesh patterns in 132-avoiding permutations I

2012-01-30

arxiv.org/abs/1201.6243v1

Mathematics

Combinatorics

35 pages, 5 figures

Scientific paper

This paper is a continuation of the systematic study of the distributions of simple marked mesh patterns initiated in \cite{kitrem}. We study simple marked mesh patterns on 132-avoiding permutations. We derive generating functions for the number of occurrences of 4-parameter simple marked mesh patterns where only one parameter is allowed to be non-zero or a non-empty set. We show that specializations of such generating functions count a number of classical combinatorial sequences. Generating functions for the number of occurrences of 4-parameter simple marked mesh patterns where two or more of the parameters are allowed to be non-zero are studied in the upcoming paper \cite{kitremtie}.

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