Maximal degree subposets of \(\nu\)-Tamari lattices
The electronic journal of combinatorics, Tome 30 (2023) no. 2
In this paper, we study two different subposets of the $\nu$-Tamari lattice: one in which all elements have maximal in-degree and one in which all elements have maximal out-degree. The maximal in-degree and maximal out-degree of a $\nu$-Dyck path turns out to be the size of the maximal staircase shape path that fits weakly abo ve $\nu$. For $m$-Dyck paths of height $n$, we further show that the maximal out-degree poset is poset isomorphic to the $\nu$-Tamari lattice of $(m-1)$-Dyck paths of height $n$, and the maximal in-degree poset is poset isomorphic to the $(m-1)$-Dyck paths of height $n$ together with a greedy order. We show these two isomorphisms and give some properties on $\nu$-Tamari lattices along the way.
DOI :
10.37236/11571
Classification :
06A07, 05A19, 06B99
Affiliations des auteurs :
Aram Dermenjian 1
@article{10_37236_11571,
author = {Aram Dermenjian},
title = {Maximal degree subposets of {\(\nu\)-Tamari} lattices},
journal = {The electronic journal of combinatorics},
year = {2023},
volume = {30},
number = {2},
doi = {10.37236/11571},
zbl = {7702599},
url = {http://geodesic.mathdoc.fr/articles/10.37236/11571/}
}
Aram Dermenjian. Maximal degree subposets of \(\nu\)-Tamari lattices. The electronic journal of combinatorics, Tome 30 (2023) no. 2. doi: 10.37236/11571
Cité par Sources :