The Electronic Journal of Combinatorics· 2026Q1
Proof of a Conjecture of Matherne, Morales, and Selover on Encodings of Unit Interval Orders
- 2citations
- Q1SCImago
- 2026year
Short summary
A conjecture by Matherne, Morales, and Selover is proven: two distinct Dyck path encodings of unit interval orders are related by Haglund's zeta bijection.
AI-generated from the title and abstract; the full text is not read.
Key points
- Proves the conjecture that two Dyck path encodings of unit interval orders are related by Haglund's zeta bijection.
- The first encoding considers pairs of incomparable elements as boxes between a Dyck path and the diagonal.
- The second encoding uses a specific part listing (Guay-Paquet, Rowland, Morales) interpreted as the area sequence of a Dyck path.
- The proof establishes a direct link between these two combinatorial objects.
AI-generated from the title and abstract; the full text is not read.
Abstract
There are two bijections from unit interval orders on $n$ elements to Dyck paths from $(0,0)$ to $(n,n)$. One is to consider the pairs of incomparable elements as forming the set of boxes between a Dyck path and the diagonal. Another is to find a particular part listing (in the sense of Guay-Paquet, Rowland and Morales) which yields an isomorphic poset, and to interpret the part listing as the area sequence of a Dyck path. Matherne, Morales, and Selover conjectured that, for any unit interval order, these two Dyck paths are related by Haglund's well-known zeta bijection. In this paper we prove their conjecture.
The authors' abstract, as published at the source. The Electronic Journal of Combinatorics, 2026 · DOI ↗
Continue with a free account
Ask the paper: 3 free questions a day about this paper; save it, get its citation, new summaries every day for your field. Takeaways are Premium.
Continue free on the webSign in with Google or Apple; no card needed. You come back to this paper.
On your phone:
Field: Discrete Mathematics and Combinatorics
Discrete Mathematics and CombinatoricsMathematics