论文标题
$ν$ -TAMARI LATTICES的最大程度子
Maximal degree subposets of $ν$-Tamari lattices
论文作者
论文摘要
在本文中，我们研究了$ν$ -tamari晶格的两个不同的子镜头：其中一个元素具有最大程度的元素，并且所有元素都具有最大程度的高度。 $ν$ -DYCK路径的最大程度和最大级别被证明是最大楼梯形状路径的大小，该路径符合$ν$的最大楼梯形状路径。 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.我们展示了这两个同构，并在此过程中赋予$ν$ -tamari晶格的一些属性。
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.
