Enumerations of bargraphs with respect to corner statistics

Abstract

We study the enumeration of bargraphs with respect to some corner statistics. We find generating functions for the number of bargraphs that tracks the corner statistics of interest, the number of cells, and the number of columns. The bargraph representation of set partitions is also considered and some explicit formulas are obtained for the number of some specific types of corners in such representations.2010 Mathematics Subject Classification. 05A18.

Enumeration of Fuss-skew paths

“…For example, the path given in Figure 5 has 4 corners, depicted in red. This statistic has been studied in other combinatorial structures as integer partitions [3], compositions [10], and bargraphs [12]. Let 𝜏 (𝑃 ) denote the number of corners of 𝑃 .…”