Applying the Cluster Method to Count Occurrences of Generalized Permutation Patterns

Details Applying the Cluster Method to Count Occurrences of Generalized Permutation Patterns Applying the Cluster Method to Count Occurrences of Generalized Permutation Patterns

2009-05-29

arxiv.org/abs/0905.4758v1

Mathematics

Combinatorics

Maple package available for download: http://math.rutgers.edu/~baxter/ClusterGPP/index.html

Scientific paper

We apply ideas from the cluster method to q-count the permutations of a multiset according to the number of occurrences of certain generalized patterns, as defined by Babson and Steingrimsson. In particular, we consider those patterns with three letters and one internal dash, as well as permutation statistics composed of counting the number of occurrences of multisets of such patterns. Counting is done via recurrences which simplify in the case of permutations. A collection of Maple procedures implementing these recurrences accompanies the article.

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