On Pattern-Avoiding Fishburn Permutations

Research output: Chapter in Book/Report/Conference proceedingChapter

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 aWilf 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)
Title of host publicationTrends in Mathematics
PublisherSpringer Science and Business Media Deutschland GmbH
Pages431-446
Number of pages16
DOIs
StatePublished - 2021

Publication series

NameTrends in Mathematics
ISSN (Print)2297-0215
ISSN (Electronic)2297-024X

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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