Peaks in Bargraphs

Abstract

Bargraphs are specific polyominoes or lattice paths in . They start at the origin and end on the -axis. The allowed steps are the up step , the down step and the horizontal step . There are a few restrictions: the first step has to be an up step and the horizontal steps must all lie above the -axis. An up step cannot follow a down step and vice versa. In this paper, we define peaks and consider various parameters relating to peaks. We find the generating functions that count these parameters and then find the mean for each statistic. We also compute the asymptotics of these means as the length of the semi-perimeter of the bargraph tends to infinity, where the semi-perimeter is the sum of all the up and horizontal steps.

Keywords:

• bargraphs
• peaks
• generating functions
• asymptotics

Additional information

Funding

This material is based upon work supported by the National Research Foundation under grant numbers 86329 and 81021 respectively.