Tony Guttmann

Self-avoiding walks and polygons crossing a domain on the square and hexagonal lattices

Anthony J Guttmann, Iwan Jensen

Journal article  |  2022  |  JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL

We have analysed the recently extended series for the number of self-avoiding walks (SAWs) C L ( 1 ) that cross an L × L square be..

Self-avoiding walks contained within a square

Anthony J Guttmann, Iwan Jensen, Aleksander L Owczarek

Journal article  |  2022  |  JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL

We have studied self-avoiding walks contained within an L × L square whose end-points can lie anywhere within, or on, the boundari..

On the existence of critical exponents for self-avoiding walks

Anthony J Guttmannl, Iwan Jensen

Journal article  |  2022  |  JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL

We describe some ideas of John Hammersley for proving the existence of critical exponents for two-dimensional self-avoiding walks ..

Pattern-Avoiding Ascent Sequences of Length 3

AR Conway, M Conway, AE Price, AJ Guttmann

Journal article  |  2022  |  Electronic Journal of Combinatorics

Pattern-avoiding ascent sequences have recently been related to set-partition problems and stack-sorting problems. While the gener..

Classical Length-5 Pattern-Avoiding Permutations

N Clisby, AR Conway, AJ Guttmann, Y Inoue

Journal article  |  2022  |  Electronic Journal of Combinatorics

We have made a systematic numerical study of the 16 Wilf classes of length-5 classical pattern-avoiding permutations from their ge..

Asymptotics of 3-Stack-Sortable Permutations

Colin Defant, Andrew Elvey Price, Anthony J Guttmann

Journal article  |  2021  |  ELECTRONIC JOURNAL OF COMBINATORICS

We derive a simple functional equation with two catalytic variables characteris-ing the generating function of 3-stack-sortable pe..

Stieltjes moment sequences for pattern-avoiding permutations

Alin Bostan, Andrew Elvey Price, Anthony John Guttmann, Jean-Marie Maillard

Journal article  |  2020  |  ELECTRONIC JOURNAL OF COMBINATORICS

A small set of combinatorial sequences have coefficients that can be represented as moments of a nonnegative measure on [0, ∞). Su..

Statistical Mechanics of Confined Polymer Networks

Bertrand Duplantier, Anthony J Guttmann

Journal article  |  2020  |  JOURNAL OF STATISTICAL PHYSICS

We show how the theory of the critical behaviour of d-dimensional polymer networks of arbitrary topology can be generalized to the..

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..

SanD primes and numbers

FJ Dyson, NE Frankel, AJ Guttmann

Journal article  |  2020  |  Journal of Integer Sequences