Bargraphs in bargraphs

Authors : TOUFIK MANSOUR, Armend SHABANI

Pages : 2763-2773

View : 21 | Download : 5

Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :Bargraphs are lattice paths in $\mathbb{N}_0^2$ that start at the origin and end upon their first return to the $x$-axis. Each bargraph is represented by a sequence of column heights $\pi_1\pi_2\cdots\pi_m$ such that column $j$ contains $\pi_j$ cells. In this paper, we study the number of bargraphs with $n$ cells and $m$ columns according to the distribution for the statistic that records the number of times a given shape lies entirely within a bargraph for various small shapes.
Keywords : Bargraphs, generating functions, C vertices, combinatorial statistic