The F-signature of Determinantal Rings

Let $R_{n,p}$ be the determinantal hypersurface ring defined by the determinant of a generic $n \times n$ matrix in characteristic $p$ where $n \geq 2$. In this paper, we obtain explicit bounds for the $F$-signature of $R_{n,p}$. For the upper bound, we prove that this $F$-signature is decreasing in