9 citations · 17 across the 10 of their papers we have counts for
12 papers
Generalised Biracks and the Birack Polynomial Invariant
Andrew Bartholomew, Roger Fenn, Louis Kauffman
We generalise the finite biquandle colouring invariant to a polynomial invariant based on labelling a knot diagram with a finite birack that reduces to the biquandle colouring inva…
Planar Doodles: Their Properties, Codes and Classification
Andrew Bartholomew, Roger Fenn
We present those properties of planar doodles, especially when regarded as 4-valent graphs, that enable us to classify them into {\it prime} and {\it super prime} doodles by analog…
Doodles and commutator identities
Andrew Bartholomew, Roger Fenn, Naoko Kamada +1
A doodle is a collection of immersed circles without triple intersections in the -sphere. It was shown by the second author and P.~Tayler that doodles induce commutator identiti…
Alexander and Markov Theorems for Generalized Knots, I
Andrew Bartholomew, Roger Fenn
In this paper we look at which Alexander and Markov theories can be defined for generalized knot theories
Colorings and doubled colorings of virtual doodles
Andrew Bartholomew, Roger Fenn, Naoko Kamada +1
A virtual doodle is an equivalence class of virtual diagrams under an equivalence relation generated by flat version of classical Reidemesiter moves and virtual Reidemsiter moves s…
On Gauss codes of virtual doodles
Andrew Bartholomew, Roger Fenn, Naoko Kamada +1
We discuss Gauss codes of virtual diagrams and virtual doodles. The notion of a left canonical Gauss code is introduced and it is shown that oriented virtual doodles are uniquely p…