38 citations · 218 across the 29 of their papers we have counts for
29 papers
Ascending Convex Polyominoes
Nicholas Beaton, Simone Rinaldi
Convex polyominoes can be refined according to the number of direction changes in monotone paths connecting pairs of cells, leading to the notion of -convexity. In particular, t…
Completing the enumeration of inversion sequences avoiding triples of relations
Nathan Britt, Nicholas Beaton
An inversion sequence of length is an integer sequence such that for all . The study of pattern-avoiding inversion sequences was initiat…
Chemical distance for the half-orthant model
Nicholas Beaton, Mark Holmes, Xin Huang
The half-orthant model is a partially oriented model of a random medium involving a parameter , for which there is a critical value (depending on the dimension…
Exact solution of weighted partially directed walks crossing a square
Nicholas R. Beaton, Aleksander L. Owczarek
We consider partially directed walks crossing a square weighted according to their length by a fugacity . The exact solution of this model is computed in three diffe…
The mean square displacement of random walk on the Manhattan lattice
Nicholas R. Beaton, Mark Holmes
We give an explicit formula for the mean square displacement of the random walk on the -dimensional Manhattan lattice after steps, for all and all dimensions .
Entanglement statistics of polymers in a lattice tube and unknotting of 4-plats
Nicholas R. Beaton, Kai Ishihara, Mahshid Atapour +4
The Knot Entropy Conjecture states that the exponential growth rate of the number of -edge lattice polygons with knot-type is the same as that for unknot polygons. Moreover,…
Walks obeying two-step rules on the square lattice: full, half and quarter planes
Nicholas R. Beaton
We consider walks on the edges of the square lattice which obey \emph{two-step rules,} which allow (or forbid) steps in a given direction to be followed by steps in a…
Exact solutions of directed walk models of polymeric zipping with pulling in two and three dimensions
Nicholas R. Beaton, Aleksander L. Owczarek
We provide the exact solution of several variants of simple models of the zipping transition of two bound polymers, such as occurs in DNA/RNA, in two and three dimensions using pai…
Semi-flexible directed polymers in a strip with attractive walls
Nicholas R. Beaton, Leo Li, Jonathon Liu +1
We study a model of a semiflexible long chain polymer confined to a two-dimensional slit of width , and interacting with the walls of the slit. The interactions with the walls a…
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…
Alignment percolation
Nicholas R. Beaton, Geoffrey R. Grimmett, Mark Holmes
The existence (or not) of infinite clusters is explored for two stochastic models of intersecting line segments in dimensions. Salient features of the phase diagram are e…
Quarter-plane lattice paths with interacting boundaries: the Kreweras and reverse Kreweras models
Nicholas R. Beaton, Aleksander L. Owczarek, Ruijie Xu
Lattice paths in the quarter plane have led to a large and varied set of results in recent years. One major project has been the classification of step sets according to the proper…
Knotting statistics for polygons in lattice tubes
Nicholas R. Beaton, Jeremy W. Eng, Christine E. Soteros
We study several related models of self-avoiding polygons in a tubular subgraph of the simple cubic lattice, with a particular interest in the asymptotics of the knotting statistic…
Enumerating five families of pattern-avoiding inversion sequences; and introducing the powered Catalan numbers
Nicholas R. Beaton, Mathilde Bouvel, Veronica Guerrini +1
The first problem addressed by this article is the enumeration of some families of pattern-avoiding inversion sequences. We solve some enumerative conjectures left open by the foun…
Exact solution of some quarter plane walks with interacting boundaries
Nicholas R Beaton, Aleksander L Owczarek, Andrew Rechnitzer
The set of random walks with different step sets (of short steps) in the quarter plane has provided a rich set of models that have profoundly different integrability properties. In…
Characterising knotting properties of polymers in nanochannels
Nicholas R. Beaton, Jeremy W. Eng, Kai Ishihara +2
Using a lattice model of polymers in a tube, we define one way to characterise different configurations of a given knot as either "local" or "non-local" and, for several ring polym…
Partition function zeros of adsorbing Dyck paths
NR Beaton, EJ Janse van Rensburg
The zeros of the size- partition functions for a statistical mechanical model can be used to help understand the critical behaviour of the model as . Here we use wei…
Adsorbing staircase polygons subject to a force
Nicholas R. Beaton
We study several models of staircase polygons on the rotated square lattice, which interact with an impenetrable surface while also being pushed towards or pulled away f…
On consecutive pattern-avoiding permutations of length 4, 5 and beyond
Nicholas R Beaton, Andrew R Conway, Anthony J Guttmann
We review and extend what is known about the generating functions for consecutive pattern-avoiding permutations of length 4, 5 and beyond, and their asymptotic behaviour. There are…
Polygons in restricted geometries subjected to infinite forces
Nicholas R Beaton, Jeremy W Eng, Christine E Soteros
We consider self-avoiding polygons in a restricted geometry, namely an infinite tube in . These polygons are subjected to a force , parallel to the infi…
Slicings of parallelogram polyominoes: Catalan, Schröder, Baxter, and other sequences
Nicholas R. Beaton, Mathilde Bouvel, Veronica Guerrini +1
We provide a new succession rule (i.e. generating tree) associated with Schröder numbers, that interpolates between the known succession rules for Catalan and Baxter numbers. We de…
A solvable non-directed model of polymer adsorption
Nicholas R. Beaton, Gerasim K. Iliev
Prudent walks are self-avoiding walks which cannot step towards an already occupied vertex. We introduce a new model of adsorbing prudent walks on the square lattice, which start o…
Compressed self-avoiding walks, bridges and polygons
Nicholas R. Beaton, Anthony J. Guttmann, Iwan Jensen +1
We study various self-avoiding walks (SAWs) which are constrained to lie in the upper half-plane and are subjected to a compressive force. This force is applied to the vertex or ve…
Adsorption of self-avoiding walks at a defect
Nicholas R. Beaton
We consider the model of self-avoiding walks on the -dimensional hypercubic lattice interacting with a -dimensional defect, where . Such an interaction can be…