Enumerations of bargraphs with respect to corner statistics

TL;DR

This paper develops generating functions to enumerate bargraphs based on corner statistics, cells, and columns, and explores their representation of set partitions with explicit formulas for specific corner types.

Contribution

It introduces new generating functions for bargraph enumeration considering corner statistics and analyzes their application to set partition representations.

Findings

Derived generating functions for corner statistics in bargraphs

Obtained explicit formulas for specific corner types in set partition representations

Connected corner statistics with bargraph enumeration and set partitions

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.