English

Noncrossing Partition Lattices from Planar Configurations

Combinatorics 2024-09-17 v2

Abstract

The lattice of noncrossing partitions is well-known for its wide variety of combinatorial appearances and properties. For example, the lattice is rank-symmetric and enumerated by the Catalan numbers. In this article, we introduce a large family of new noncrossing partition lattices with both of these properties, each parametrized by a configuration of n points in the plane.

Keywords

Cite

@article{arxiv.2306.08119,
  title  = {Noncrossing Partition Lattices from Planar Configurations},
  author = {Stella Cohen and Michael Dougherty and Andrew D. Harsh and Spencer Park Martin},
  journal= {arXiv preprint arXiv:2306.08119},
  year   = {2024}
}

Comments

30 pages, 21 figures. Expanded exposition and fixed errors in Propositions 2.3 and 4.4. Final version

R2 v1 2026-06-28T11:04:27.388Z