2022/08/24 by Aram Dermenjian, Dermenjian, Aram
Computer Science · Mathematics · #05A19 #05E #06A07 #Advanced Algebra and Logic #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2208.11417
openalex publication_date 2022/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
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.