Catalan intervals and uniquely sorted permutations

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:174

Article

Defant, Colin¹ 

[1] Princeton Univ, Fine Hall,304 Washington Rd, Princeton, NJ 08544 USA

关键词: Uniquely sorted permutation;    Poset interval;    Dyck path;    Stanley lattice;    Tamari lattice;    Noncrossing partition lattice;    Pallo comb poset;    Stack-sorting;   

DOI  :  10.1016/j.jcta.2020.105250

来源: Elsevier

【 摘 要 】

For each positive integer k, we consider five well-studied posets defined on the set of Dyck paths of semilength k. We prove that uniquely sorted permutations avoiding various patterns are equinumerous with intervals in these posets. While most of our proofs are bijective, some use generating trees and generating functions. We end with several conjectures. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free