t-Bargraphs and t-compositions

Abstract

In this paper, we consider several statistics on t-compositions. We exhibit a bijection between the set of t-compositions and a set of bargraphs, introduced in this paper, named t-bargraphs. As our main statistic is per { the perimeter of a given t-bargraph, we obtain the corresponding generating function. We nd both an explicit and an asymptotic formula for the total length of the perimeter over all t-bargraphs with n-cells.

Key words: t-bargraphs, t-compositions.