2018/03/19 by Harrison Chapman, Chapman, Harrison
Mathematics · Computer Science · #Geometric and Algebraic Topology #Advanced Combinatorial Mathematics #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1803.07114
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 chains in space. As an alternative to space curves, we provide a framework for working with subknots inside of knot diagrams via knotoid diagrams. We prove using a pattern theorem for knot diagrams that not only are almost all knot diagrams slipknotted, almost all unknot diagrams are slipknotted. This proves in the random diagram model a conjecture yet unproven in random space curve models. We also discuss conjectures on the enumeration of knotoid diagrams.