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arXiv · 1812.01682

On pattern-avoiding Fishburn permutations

Juan B. Gil·Michael D. Weiner
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Abstract

The class of permutations that avoid the bivincular pattern (231, {1},{1}) is known to be enumerated by the Fishburn numbers. In this paper, we call them Fishburn permutations and study their pattern avoidance. For classical patterns of size 3, we give a complete enumerative picture for regular and indecomposable Fishburn permutations. For patterns of size 4, we focus on a Wilf equivalence class of Fishburn permutations that are enumerated by the Catalan numbers. In addition, we also discuss a class enumerated by the binomial transform of the Catalan numbers and give conjectures for other equivalence classes of pattern-avoiding Fishburn permutations.

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Juan B. Gil, Michael D. Weiner. 2018-12-04. On pattern-avoiding Fishburn permutations. https://arxiv.org/abs/1812.01682

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