21 citations · 72 across the 17 of their papers we have counts for
19 papers
Primality of theta-curves with proper rational tangle unknotting number one
Kenneth L. Baker, Dorothy Buck, Danielle O'Donnol +2
We show that if a composite -curve has (proper rational) unknotting number one, then it is the order 2 sum of a (proper rational) unknotting number one knot and a trivial -cu…
Integrating Transposable Elements in the 3D Genome
Alexandros Bousios, Hans-Wilhelm Nuetzmann, Dorothy Buck +1
Chromosome organisation is increasingly recognised as an essential component of genome regulation, cell fate and cell health. Within the realm of transposable elements (TEs) howeve…
Grid diagrams as tools to investigate knot spaces and topoisomerase-mediated simplification of DNA topology
Agnese Barbensi, Daniele Celoria, Heather A. Harrington +2
Grid diagrams with their relatively simple mathematical formalism provide a convenient way to generate and model projections of various knots. It has been an open question whether…
Double branched covers of knotoids
Agnese Barbensi, Dorothy Buck, Heather A. Harrington +1
By using double branched covers, we prove that there is a 1-1 correspondence between the set of knotoids in the 2-sphere, up to orientation reversion and rotation, and knots with a…
Unknotting numbers for prime -curves up to seven crossings
Dorothy Buck, Danielle O'Donnol
Determining unknotting numbers is a large and widely studied problem. We consider the more general question of the unknotting number of a spatial graph. We show the unknotting numb…
Toroidal embeddings of abstractly planar graphs are knotted or linked
Senja Barthel, Dorothy Buck
We give explicit deformations of embeddings of abstractly planar graphs that lie on the standard torus and that contain neither a nontrivial knot nor a n…