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Vincular Pattern Posets and the Möbius Function of the Quasi-Consecutive Pattern Poset

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Abstract

We introduce vincular pattern posets, then we consider in particular the quasiconsecutive pattern poset, which is defined by declaring σ ≤ τ whenever the permutation τ contains an occurrence of the permutation σ in which all the entries are adjacent in τ except at most the first and the second. We investigate the Möbius function of the quasi-consecutive pattern poset and we completely determine it for those intervals [σ, τ] such that σ occurs precisely once in τ.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica “U. Dini”, University of Firenze, viale Morgagni 65, Firenze, Italy

    Antonio Bernini & Luca Ferrari

Authors
  1. Antonio Bernini
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  2. Luca Ferrari
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Correspondence to Luca Ferrari.

Additional information

Antonio Bernini and Luca Ferrari: Partially supported by MIUR PRIN 2010-2011 grant “Automi e Linguaggi Formali: Aspetti Matematici e Applicativi", code H41J12000190001.

Luca Ferrari: Partially supported by INdAM-GNCS 2014 project “Studio di pattern in strutture combinatorie".

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Bernini, A., Ferrari, L. Vincular Pattern Posets and the Möbius Function of the Quasi-Consecutive Pattern Poset. Ann. Comb. 21, 519–534 (2017). https://doi.org/10.1007/s00026-017-0364-y

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  • DOI: https://doi.org/10.1007/s00026-017-0364-y

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