The Priority Lattice
Combinatorics
2026-04-01 v1
Abstract
We introduce the priority lattice, a structure arising from the priority search algorithm on rooted trees and forests. We prove bijectively that its maximal chains are labeled by parking functions, and that the maximal chains of its principal ideals are labeled by partial parking functions. We establish that it is a graded lattice and compute its M\"obius function and characteristic polynomials.
Cite
@article{arxiv.2603.28905,
title = {The Priority Lattice},
author = {Adrián Lillo and Mercedes Rosas},
journal= {arXiv preprint arXiv:2603.28905},
year = {2026}
}
Comments
26 pages, 10 figures