• Corpus ID: 251765453

Maximal degree subposets of $\nu$-Tamari lattices

@inproceedings{Dermenjian2022MaximalDS,
  title={Maximal degree subposets of \$\nu\$-Tamari lattices},
  author={Aram Dermenjian},
  year={2022}
}

• Aram Dermenjian
• Published 24 August 2022
• Mathematics

. In this paper, we study two different subposets of the ν -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 ν -Dyck path turns out to be the size of the maximal staircase shape path that fits weakly above ν . For m -Dyck paths of height n , we further show that the maximal out-degree poset is poset isomorphic to the ν -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 ν -Tamari lattices along the way.