Bijective proof of a conjecture on unit interval posets

Abstract

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.

8 pages, 3 figures. Accepted by Discrete Mathematics & Theoretical Computer Science

References in corpus (2)

• The Newton polytope and Lorentzian property of chromatic symmetric functions
• Proof of a conjecture of Matherne, Morales, and Selover on encodings of unit interval orders

Cited by in corpus (1)

• The Newton polytope and Lorentzian property of chromatic symmetric functions