38 citations · 218 across the 29 of their papers we have counts for
10 papers · 1 filter
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…
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…
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…
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…
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…
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…
The Enumeration of Prudent Polygons by Area and its Unusual Asymptotics
Nicholas R. Beaton, Philippe Flajolet, Anthony J. Guttmann
Prudent walks are special self-avoiding walks that never take a step towards an already occupied site, and \emph{-sided prudent walks} (with ) are, in essence, only a…