Polygons and stars in a slit geometry
C E Soteros, Stuart G. Whittington · Journal of Physics A Mathematical and General · 1988
The authors consider self-avoiding polygons, uniform 3-stars and uniform 4-stars, weakly embeddable in the square lattice and confined between two parallel lines, y=0 and y=L. They show rigorously that the connective constants of these three structures (provided that the corresponding limits exist) are all strictly less than the connective constant kappa (L) of self-avoiding walks, with the same geometrical constraint. They also derive lower bounds on the connective constants of uniform 3-stars and 4-stars. These bounds appear to be strong, at least for small L.