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

Fuente: arXiv
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Main Authors: Elizalde, Sergi, Lafrenière, Nadia, Lewis, Joel Brewster, McNicholas, Erin, Striker, Jessica, Welch, Amanda
Format: Preprint
Published: 2024
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_version_ 1866915074944270336
author Elizalde, Sergi
Lafrenière, Nadia
Lewis, Joel Brewster
McNicholas, Erin
Striker, Jessica
Welch, Amanda
author_facet Elizalde, Sergi
Lafrenière, Nadia
Lewis, Joel Brewster
McNicholas, Erin
Striker, Jessica
Welch, Amanda
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2412_16368
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Enumeration of interval-closed sets via Motzkin paths and quarter-plane walks
Elizalde, Sergi
Lafrenière, Nadia
Lewis, Joel Brewster
McNicholas, Erin
Striker, Jessica
Welch, Amanda
Combinatorics
05A15, 06A07
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.
title Enumeration of interval-closed sets via Motzkin paths and quarter-plane walks
topic Combinatorics
05A15, 06A07
url https://arxiv.org/abs/2412.16368