The Perimeter of 2-Compositions

Abstract

In this note, we consider several statistics on 2-compositions. We show that there is a bijection between the set of 2-compositions and a set of bargraphs, introduced in this note, named 2-bargraphs. As we focus on the statistic per – the perimeter of the given 2-bargraph, we find the corresponding generating function. We also find an explicit formula for the total length of the perimeter over all 2-bargraphs with n-cells.