38 citations · 218 across the 29 of their papers we have counts for
4 papers · 1 filter
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…