43 citations · 91 across the 6 of their papers we have counts for
6 papers
On trivial words in finitely presented groups
M. Elder, A. Rechnitzer, E. J. Janse van Rensburg +1
We propose a numerical method for studying the cogrowth of finitely presented groups. To validate our numerical results we compare them against the corresponding data from groups w…
Lattice Knots in a Slab
D. Gasumova, E. J. Janse van Rensburg, A. Rechnitzer
In this paper the number and lengths of minimal length lattice knots confined to slabs of width , is determined. Our data on minimal length verify the results by Sharein et.al.…
On the universality of knot probability ratios
E. J. Janse van Rensburg, A. Rechnitzer
Let denote the number of self-avoiding polygons of length on a regular three-dimensional lattice, and let be the number which have knot type . The probability…
Directed Paths in a Wedge
E J Janse van Rensburg, T Prellberg, A Rechnitzer
Directed paths have been used extensively in the scientific literature as a model of a linear polymer. Such paths models in particular the conformational entropy of a linear polyme…
Light propagation in a Cole-Cole nonlinear medium via Burgers-Hopf equation
Boris Konopelchenko, Antonio Moro
Recently, a new model of propagation of the light through the so-called weakly three-dimensional Cole-Cole nonlinear medium with short-range nonlocality has been proposed. In parti…
Inversion relations, reciprocity and polyominoes
M. Bousquet-Melou, A. J. Guttmann, W. P. Orrick +1
We derive self-reciprocity properties for a number of polyomino generating functions, including several families of column-convex polygons, three-choice polygons and staircase poly…