Enumeration of interval-closed sets via Motzkin paths and quarter-plane walks

Journal of Combinatorics 2026 Open access

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Authors: Sergi Elizalde, Nadia Lafrenière, Joel Brewster Lewis, Erin McNicholas, Jessica Striker, Amanda Welch
DOI: 10.4310/joc.260511231044
Cited by: 0

Abstract

We find a generating function for interval-closed sets of the product of two chains poset by constructing a bijection to certain bicolored Motzkin paths. We also find a functional equation for the generating function of interval-closed sets of truncated rectangle posets, including the type A root poset, by constructing a bijection to certain quarter-plane walks.

Fields of Study & Subjects

Advanced Combinatorial Mathematics Topological and Geometric Data Analysis Constraint Satisfaction and Optimization

Publication details

Journal / source
Journal of Combinatorics
Publisher
International Press of Boston
Volume
17
Issue
4
Pages
527–557
Publication date
1 January 2026
Language
EN