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.
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Gil, J.B., Weiner, M.D. (2021). On Pattern-Avoiding Fishburn Permutations. In: Alladi, K., Berndt, B.C., Paule, P., Sellers, J.A., Yee, A.J. (eds) George E. Andrews 80 Years of Combinatory Analysis. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-57050-7_25
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DOI: https://doi.org/10.1007/978-3-030-57050-7_25
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-57049-1
Online ISBN: 978-3-030-57050-7
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