Chimneys in compositions and bargraphs

Abstract

Motivated by cut points in graph theory, we consider a similar notion in compositions and bargraphs. This is equivalent to counting r -chimneys (a single column extending beyond its immediate neighbours by at least r cells in a bargraph). We establish generating functions for compositions that avoid or count 2 -chimneys. Thereafter, in the case of bargraphs we provide two methods for obtaining these generating functions as well as asymptotic estimates for the more general r -chimneys where r ≥ 1