Enumerative combinatorics of intervals in the Dyck pattern poset
Combinatorics
2019-10-02 v1
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 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.
Keywords
Cite
@article{arxiv.1910.00299,
title = {Enumerative combinatorics of intervals in the Dyck pattern poset},
author = {Antonio Bernini and Matteo Cervetti and Luca Ferrari and Einar Steingrimsson},
journal= {arXiv preprint arXiv:1910.00299},
year = {2019}
}
Comments
14 pages, 3 figures