Abstract
A bargraph is a lattice path in N02 with three allowed steps: the up step u=(0,1), the down step d=(0,−1) and the horizontal step h=(1,0). It starts at the origin with an up step and terminates as soon as it intersects the x-axis again. A down step cannot follow an up step and vice versa. The height of a bargraph is the maximum y coordinate attained by the graph. The width is the horizontal distance from the origin till the end. For bargraphs of fixed semi-perimeter n we find the generating functions for the total height and the total width and hence find asymptotic estimates for the average height and the average width. Our methodology makes use of a bijection between bargraphs and uudd-avoiding Dyck paths.
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