Enumerative combinatorics of intervals in the Dyck pattern poset

Bernini, Antonio and Cervetti, Matteo and Ferrari, Luca and Steingrímsson, Einar (2021) Enumerative combinatorics of intervals in the Dyck pattern poset. Order. ISSN 0167-8094

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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.

    ORCID iDs

    Bernini, Antonio, Cervetti, Matteo, Ferrari, Luca and Steingrímsson, Einar ORCID logoORCID: https://orcid.org/0000-0003-4611-0849;