A bijective proof of an identity of Berkovich and Uncu

Aritram Dhar, Avi Mukhopadhyay

The BG-rank BG($\pi$) of an integer partition $\pi$ is defined as $$\text{BG}(\pi ):=i-j$$ where $i$ is the number of odd-indexed odd parts and $j$ is the number of even-indexed odd par…