I actually know that the answer is $N(k1)$ (where $k$ is the minimum between number of rows and number of columns).
However, I can not seem to find a simple proof for why the statistic is bounded by this. Any suggestions (or references?)
I actually know that the answer is $N(k1)$ (where $k$ is the minimum between number of rows and number of columns). However, I can not seem to find a simple proof for why the statistic is bounded by this. Any suggestions (or references?) 

