181 citations · 1.9k across the 66 of their papers we have counts for
66 papers
The gerrymander sequence, or A348456
Anthony J Guttmann, Iwan Jensen
Recently Kauers, Koutschan and Spahn announced a significant increase in the length of the so-called {\em gerrymander sequence}, given as A348456 in the OEIS, extending the sequenc…
Self-avoiding walks and polygons crossing a domain on the square and hexagonal lattices
Anthony J Guttmann, Iwan Jensen
We have analysed the recently extended series for the number of self-avoiding walks (SAWs) that cross an square between diagonally opposed corners. The number…
Self-avoiding walks contained within a square
Anthony J Guttmann, Iwan Jensen, Aleksander L Owczarek
We have studied self-avoiding walks contained within an square whose end-points can lie anywhere within, or on, the boundaries of the square. We prove that such walks…
On the existence of critical exponents for self-avoiding walks
Anthony J Guttmann, Iwan Jensen
We describe some ideas of John Hammersley for proving the existence of critical exponents for two-dimensional self-avoiding walks and provide numerical evidence for their correctne…
Two-dimensional interacting self-avoiding walks: new estimates for critical temperatures and exponents
Nicholas R Beaton, Anthony J Guttmann, Iwan Jensen
We investigate, by series methods, the behaviour of interacting self-avoiding walks (ISAWs) on the honeycomb lattice and on the square lattice. This is the first such investigation…
Polygons pulled from an adsorbing surface
AJ Guttmann, EJ Janse van Rensburg, I Jensen +1
We consider self-avoiding lattice polygons, in the hypercubic lattice, as a model of a ring polymer adsorbed at a surface and either being desorbed by the action of a force, or pus…