Circular bargraphs

摘要

In this paper, we introduce a new class of bargraphs – circular bargraphs, which are self-avoiding walks in a cylindrical lattice, and study the enumerations of them with respect to perimeter statistic. More precisely, we study the perimeter of a circular bargraph, a statistic defined naturally as the number of edges in the boundary of the bargraph. We also find an explicit formula for the total length of the perimeter over all bargraphs with n-cells.