Report
Maximal degree subposets of $\nu$-Tamari lattices
| العنوان: | Maximal degree subposets of $\nu$-Tamari lattices |
|---|---|
| المؤلفون: | Dermenjian, Aram |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, 05E, 05A19, 06A07 |
| الوصف: | 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 above $\nu$.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. Comment: 34 pages, 3 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2208.11417 |
| رقم الانضمام: | edsarx.2208.11417 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |