4 papers
Geometric Combinatorics of Polynomials I: The Case of a Single Polynomial
Michael Dougherty, Jon McCammond
There are many different algebraic, geometric and combinatorial objects that one can attach to a complex polynomial with distinct roots. In this article we introduce a new object t…
Critical Points, Critical Values, and a Determinant Identity for Complex Polynomials
Michael Dougherty, Jon McCammond
Given any n-tuple of complex numbers, one can canonically define a polynomial of degree n+1 that has the entries of this n-tuple as its critical points. In 2002, Beardon, Carne, an…
Boundary Braids
Michael Dougherty, Jon McCammond, Stefan Witzel
The n-strand braid group can be defined as the fundamental group of the configuration space of n unlabeled points in a closed disk based at a configuration where all n points lie i…
Undesired parking spaces and contractible pieces of the noncrossing partition link
Michael Dougherty, Jon McCammond
There are two natural simplicial complexes associated to the noncrossing partition lattice: the order complex of the full lattice and the order complex of the lattice with its boun…