Enumerative combinatorics of intervals in the Dyck pattern poset

Autor:	Bernini, Antonio, Cervetti, Matteo, Ferrari, Luca, Steingrimsson, Einar
Rok vydání:	2019
Předmět:	Mathematics - Combinatorics
Druh dokumentu:	Working Paper
Popis:	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 M\"obius function of the Dyck pattern poset, giving for instance a closed expression for the M\"obius function of initial intervals whose maximum is a Dyck path having exactly two peaks. Comment: 14 pages, 3 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1910.00299 Zobrazit plný text záznamu View this record from Arxiv