Noncrossing Partition Lattices from Planar Configurations
arXiv:2306.08119 · doi:10.1007/s00454-024-00682-6
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.
30 pages, 21 figures. Expanded exposition and fixed errors in Propositions 2.3 and 4.4. Final version