On the determinants and permanents of matrices with restricted entries over prime fields

Abstract

Let $A$ be a set in a prime field ${\mathbb{F}}_p$. In this paper, we prove that $d\times d$ matrices with entries in $A$ determine almost $|A{|}^{3+\frac{1}{45}}$ distinct determinants and almost $|A{|}^{2-\frac{1}{6}}$ distinct permanents when $|A|$ is small enough.

Submitted for publication

References in corpus (1)

• An Improved Point-Line Incidence Bound Over Arbitrary Fields

Cited by in corpus (2)

• Expanding phenomena over higher dimensional matrix rings
• Counting matrices over finite rank multiplicative groups