Permutations with a fixed number of occurrences of a pattern: A case generalizing 231

Michael Waite

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arXiv · 2603.21625

Permutations with a fixed number of occurrences of a pattern: A case generalizing 231

Michael Waite

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Abstract

We determine a set of permutation patterns $q$ so that the number of permutations with $r$ occurrences of $q$ is asymptotically $n^r$ times the number of permutations avoiding $q$, partially settling a conjecture of Conway and Guttman. We also use these asymptotics to prove nonrationality and nonalgebraicity for certain ordinary generating functions for permutations with $r$ copies of a pattern.

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Michael Waite. 2026-06-09. Permutations with a fixed number of occurrences of a pattern: A case generalizing 231. https://arxiv.org/abs/2603.21625

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