On the rank of $n\times n$ matrix multiplication

Alex Massarenti, Emanuele Raviolo

For every $p\le n$ positive integer we obtain the lower bound $(3-\frac{1}{p+1})n^2-\left(2\right(\genfrac{}{}{0ex}{}{2p}{p+1})-(\genfrac{}{}{0ex}{}{2p-2}{p-1})+2)n$ for the rank of the $n\times n$ matrix multipl…