Noncrossing Partitions From Cones and Semicircles
Combinatorics
2026-04-17 v1
Abstract
For each finite configuration of distinct points in the plane, there is an associated lattice of noncrossing partitions. When these points form the vertices of a convex polygon, the result is the classical noncrossing partition lattice, which is enumerated by the Catalan numbers and satisfies many other useful properties. In this article, we examine three variations of this lattice which arise when the starting configuration is allowed to have points on the sides of a convex polygon rather than just the vertex set.
Cite
@article{arxiv.2604.14462,
title = {Noncrossing Partitions From Cones and Semicircles},
author = {Michael Dougherty and Kaiyi Fang and Yunting Jiang and Edgar Lin and Lucas Lindenmuth and Eleanor Pokras and Gina Root},
journal= {arXiv preprint arXiv:2604.14462},
year = {2026}
}
Comments
17 pages, 5 figures. Final version