Article Dans Une Revue Discrete Mathematics and Theoretical Computer Science Année : 2024

Bijective proof of a conjecture on unit interval posets

Résumé

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.

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hal-04486630 , version 1 (02-03-2024)

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Wenjie Fang. Bijective proof of a conjecture on unit interval posets. Discrete Mathematics and Theoretical Computer Science, 2024, vol. 26:2 (Combinatorics), ⟨10.46298/dmtcs.10837⟩. ⟨hal-04486630⟩
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