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arXiv · 1102.2480

Computational Approaches to Consecutive Pattern Avoidance in Permutations

Brian Nakamura
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Abstract

In recent years, there has been increasing interest in consecutive pattern avoidance in permutations. In this paper, we introduce two approaches to counting permutations that avoid a set of prescribed patterns consecutively. These algoritms have been implemented in the accompanying Maple package CAV, which can be downloaded from the author's website. As a byproduct of the first algorithm, we have a theorem giving a sufficient condition for when two pattern sets are strongly (consecutively) Wilf-Equivalent. For the implementation of the second algorithm, we define the cluster tail generating function and show that it always satisfies a certain functional equation. We also explain how the CAV package can be used to approximate asymptotic constants for single pattern avoidance.

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Brian Nakamura. 2011-02-12. Computational Approaches to Consecutive Pattern Avoidance in Permutations. https://arxiv.org/abs/1102.2480

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