A partial order on Motzkin paths

被引：2

作者：

Fang, Wenjie ^{[1
,2
]}

机构：

[1] Univ Paris Est Marne la Vallee, LIGM UMR 8094, CNRS, ENPC,ESIEE Paris, Paris, France

[2] Graz Univ Technol, Graz, Austria

来源：

DISCRETE MATHEMATICS | 2020年 / 343卷 / 05期

关键词：

Motzkin path; Tamari lattice; numeration of intervals; Schroder path; PLANAR MAPS; TAMARI; ENUMERATION; LATTICES;

D O I：

10.1016/j.disc.2019.111802

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Tamari lattice, defined on Catalan objects such as binary trees and Dyck paths, is a well-studied poset in combinatorics. It is thus natural to try to extend it to other families of lattice paths. In this article, we fathom such a possibility by defining and studying an analogy of the Tamari lattice on Motzkin paths. While our generalization is not a lattice, each of its connected components is isomorphic to an interval in the classical Tamari lattice. With this structural result, we proceed to the enumeration of components and intervals in the poset of Motzkin paths we defined. We also extend the structural and enumerative results to Schroder paths. We conclude by a discussion on the relation between our work and that of Baril and Pallo (2014). (C) 2019 Elsevier B.V. All rights reserved.

引用

页数：9

共 17 条

[11] The enumeration of generalized Tamari intervals [J].