Daniel Panario

We discuss constructions based on finite fields of three types of combinatorial arrays: orthogonal, covering and ordered orthogonal arrays. Other combinatorial arrays have been similarly considered in the literature, including permutation arrays...

When we iterate functions over finite structures, there is an underlying natural functional graph. For a function $f$ over a finite field $\mathbb{F}_q$, this graph has $q$ nodes and a directed edge from vertex $a$ to vertex $b$ if and only if $f(a)...