Additive Decompositions by Conjugacy Classes in $M_n({\mathbb{F}}_q)$

Krishna Kishore, Sunil Kumar Mallick

Let $n\ge 2$ be a positive integer, and $q$ be a prime power. We study the $number$ of additive decompositions of nonscalar matrices in the matrix ring $M_n({\mathbb{F}}_q)$ as sum…