A MODIFIED SELF-AVOIDING WALK MODEL ON THE SQUARE LATTICE WITH REFLECTING AND ABSORBING BARRIERS

Well known is the directed self-avoiding walk model on the square lattice with reflecting and absorbing barriers. We consider two models, namely, a pyramid self-avoiding polygon model and a top and bottom pyramid polygon model, as subcollections of the model. We derive explicit formulas for the number of 2N-step polygons in these models.