3 citations · 4 across the 8 of their papers we have counts for
11 papers
Noncrossing Partitions From Hull Configurations
Michael Dougherty, Gina Root
Each finite configuration of points in the plane determines a corresponding lattice of noncrossing partitions. When these points form the vertex set of a convex polygon, the associ…
The Geometry of Rectangular Multisets
Michael Dougherty, Jon McCammond
This article describes a natural piecewise Euclidean bi-simplicial cell structure for the space of -element multisets in a fixed Euclidean rectangle. In particular, we highlight…
Continuous Noncrossing Partitions and Weighted Circular Factorizations
Michael Dougherty, Jon McCammond
This article examines noncrossing partitions of the unit circle in the complex plane; we call these continuous noncrossing partitions. More precisely, we focus on the degree- co…
Geometric Combinatorics of Polynomials II: Polynomials and Cell Structures
Michael Dougherty, Jon McCammond
This article introduces a finite piecewise Euclidean cell complex homeomorphic to the space of monic centered complex polynomials of degree whose critical values lie in a fixed…
Noncrossing Partition Lattices from Planar Configurations
Stella Cohen, Michael Dougherty, Andrew D. Harsh +1
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 t…
The Polyhedral Tree Complex
Michael Dougherty
The tree complex is a simplicial complex defined in recent work of Belk, Lanier, Margalit, and Winarski with natural applications to mapping class groups and complex dynamics. In t…