15 citations · 31 across the 4 of their papers we have counts for
5 papers
On the Structure and Scarcity of Alternating Knots
Harrison Chapman
Given a class of objects, a pattern theorem is a powerful result describing their structure. We show that alternating knots exhibit a pattern theorem, and use this result to prove…
A Markov Chain Sampler for Plane Curves
Harrison Chapman, Andrew Rechnitzer
A plane curve is a knot diagram in which each crossing is replaced by a 4-valent vertex, and so are dual to a subset of planar quadrangulations. The aim of this paper is to introdu…
Slipknotting in Random Diagrams
Harrison Chapman
The presence of slipknots in configurations of proteins and DNA has been shown to affect their functionality, or alter it entirely. Historically, polymers are modeled as polygonal…
Asymptotic laws for random knot diagrams
Harrison Chapman
We study random knotting by considering knot and link diagrams as decorated, (rooted) topological maps on spheres and pulling them uniformly from among sets of a given number of ve…
Knot Probabilities in Random Diagrams
Jason Cantarella, Harrison Chapman, Matt Mastin
We consider a natural model of random knotting- choose a knot diagram at random from the finite set of diagrams with n crossings. We tabulate diagrams with 10 and fewer crossings a…