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.

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

• 05C05 - Trees
• 05C10 - Planar graphs; geometric and topological aspects of graph theory
• 05C38 - Paths and cycles