Enumerative combinatorics of intervals in the Dyck pattern poset

Antonio Bernini, Matteo Cervetti, Luca Ferrari, Einar Steingrímsson

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Abstract

We initiate the study of the enumerative combinatorics of the intervals in the Dyck pattern poset. More specifically, we find some closed formulas to express the size of some specific intervals, as well as the number of their covering relations. In most of the cases, we are also able to refine our formulas by rank. We also provide the first results on the Möbius function of the Dyck pattern poset, giving for instance a closed expression for the Möbius function of initial intervals whose maximum is a Dyck path having exactly two peaks.

Original languageEnglish
Number of pages15
JournalOrder
DOIs
Publication statusPublished - 3 Apr 2021

Keywords

  • Dyck path
  • enumeration
  • interval
  • Möbius function
  • poset

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