Applying the cluster method to count occurrences of generalized permutation patterns

作者：Baxter Andrew M^*

来源：Journal of Difference Equations and Applications, 2011, 17(5): 709-720.

DOI：10.1080/10236190903170706

• permutation patterns
• exact enumeration
• generating functions
• q-difference equations

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.

• 出版日期2011