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Bijective proof of a conjecture on unit interval posets

Wenjie Fang
Dec 2022
摘要
In a recent preprint, Matherne, Morales and Selover conjectured that twodifferent representations of unit interval posets are related by the famouszeta map in $q,t$-Catalan combinatorics. This conjecture was proved recently byG\'elinas, Segovia and Thomas using induction. In this short note, we provide abijective proof of the same conjecture with a reformulation of the zeta mapusing left-aligned colored trees, first proposed in the study of parabolicTamari lattices.
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