15 citations · 31 across the 4 of their papers we have counts for
Showing 2018Show all
3 papers · 1 filter
math.GT2018★ 3 cited
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…
math.CO2018
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…
math.GT2018★ 1 cited
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…