On Pattern-Avoiding Fishburn Permutations

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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.

Original languageEnglish (US)
Pages (from-to)785-800
Number of pages16
JournalAnnals of Combinatorics
Volume23
Issue number3-4
DOIs
Publication statusPublished - Nov 1 2019

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All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics

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