Tony Guttmann

Two-dimensional interacting self-avoiding walks: new estimates for critical temperatures and exponents

Nicholas R Beaton, Anthony J Guttmann, Iwan Jensen

Journal article  |  2020  |  Journal of Physics A: Mathematical and Theoretical

We investigate, by series methods, the behaviour of interacting self-avoiding walks (ISAWs) on the honeycomb lattice and on the sq..

Permutations sortable by two stacks in series

A Elvey Price, AJ Guttmann

Journal article  |  2017  |  Advances in Applied Mathematics

We address the problem of the number of permutations that can be sorted by two stacks in series. We do this by first counting all ..

Permutations sortable by deques and by two stacks in parallel

Andrew Elvey Price, Anthony J Guttmann

Journal article  |  2017  |  European Journal of Combinatorics

Recently Albert and Bousquet-Mélou (2015) obtained the solution to the long-standing problem of the number of permutations sortabl..

Is the full susceptibility of the square-lattice Ising model a differentially algebraic function?

AJ Guttmann, I Jensen, J-M Maillard, J Pantone

Journal article  |  2016  |  Journal of Physics A: Mathematical and Theoretical

We study the class of non-holonomic power series with integer coefficients that reduce, modulo primes, or powers of primes, to alg..

On the growth constant for square-lattice self-avoiding walks

Jesper Lykke Jacobsen, Christian R Scullard, Anthony J Guttmann

Journal article  |  2016  |  Journal of Physics A: Mathematical and Theoretical

The growth constant for two-dimensional self-avoiding walks on the honeycomb lattice was conjectured by Nienhuis in 1982, and sinc..

Series extension: predicting approximate series coefficients from a finite number of exact coefficients

Anthony J Guttmann

Journal article  |  2016  |  Journal of Physics A: Mathematical and Theoretical

Given the first 20-100 coefficients of a typical generating function of the type that arises in many problems of statistical mecha..

Three-dimensional terminally attached self-avoiding walks and bridges

Nathan Clisby, Andrew R Conway, Anthony J Guttmann

Journal article  |  2016  |  Journal of Physics A: Mathematical and Theoretical

We study terminally attached self-avoiding walks (SAWs) and bridges on the simple cubic lattice, both by series analysis and Monte..

Automata and the susceptibility of the square lattice Ising model modulo powers of primes

AJ Guttmann, J-M Maillard

Journal article  |  2015  |  Journal of Physics A: Mathematical and Theoretical

We study the full susceptibility of the Ising model modulo powers of primes. We find exact functional equations for the full susce..

Compressed self-avoiding walks, bridges and polygons

Nicholas R Beaton, Anthony J Guttmann, Iwan Jensen, Gregory F Lawler

Journal article  |  2015  |  JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL

We study various self-avoiding walks (SAWs) which are constrained to lie in the upper half-plane and are subjected to a compressiv..

On 1324-avoiding permutations

Andrew R Conway, Anthony J Guttmann

Journal article  |  2015  |  Advances in Applied Mathematics

We give an improved algorithm for counting the number of 1324-avoiding permutations, resulting in 5 further terms of the generatin..