Bijective proof of a conjecture on unit interval posets

In a recent preprint, Matherne, Morales and Selover conjectured that two different representations of unit interval posets are related by the famous zeta map in q, t-Catalan combinatorics. This conjecture was proved recently by Gélinas, Segovia and Thomas using induction. In this short note, we prov...

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Bibliographic Details
Published in:Discrete mathematics and theoretical computer science 2024-08, Vol.26 (2), p.1-8
Main Author: Fang, Wenjie
Format: Article
Language:English
Subjects:
Combinatorial analysis
Lattices
Set theory
Online Access:Get full text
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Summary:In a recent preprint, Matherne, Morales and Selover conjectured that two different representations of unit interval posets are related by the famous zeta map in q, t-Catalan combinatorics. This conjecture was proved recently by Gélinas, Segovia and Thomas using induction. In this short note, we provide a bijective proof of the same conjecture with a reformulation of the zeta map using left-aligned colored trees, first proposed in the study of parabolic Tamari lattices.
ISSN:1365-8050