15 citations · 15 across the 2 of their papers we have counts for
6 papers
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…
An Enhanced Decomposition Theorem for Knots with Symmetry Information
Matt Mastin
We present an enhanced prime decomposition theorem for knots that gives the isotopy classes of composite knots that can be constructed from a given list of prime factors (allowing…
Links and Planar Diagram Codes
Matt Mastin
In this paper we formalize a combinatorial object for describing link diagrams called a Planar Diagram Code. PD-codes are used by the KnotTheory Mathematica package developed by Ba…
Symmetric Criticality for Tight Knots
Jason Cantarella, Jennifer Ellis, Joseph H. G. Fu +1
We prove a version of symmetric criticality for ropelength-critical knots. Our theorem implies that a knot or link with a symmetric representative has a ropelength-critical configu…
The 27 possible intrinsic symmetry groups of two-component links
Jason Cantarella, James Cornish, Matt Mastin +1
We consider the "intrinsic" symmetry group of a two-component link , defined to be the image of the natural homomorphism from the standard symmetry group $\MCG(S^3,L)$ to…
Intrinsic symmetry groups of links with 8 and fewer crossings
Michael Berglund, Jason Cantarella, Meredith Perrie Casey +9
We present an elementary derivation of the "intrinsic" symmetry groups for knots and links of 8 or fewer crossings. The standard symmetry group for a link is the mapping class grou…