4 problems

Let $p$ be a prime, let $n$ be a positive integer, and let $bin\mathbb F_{p^n}$ satisfy $\operatorname{Tr}_{p^n/p}(b)\ne 0$. Define … A rational function is a permutation rational…

Let $q$ be a power of a prime, and let the paper's computed lower bounds for permutation-array parameters be denoted by the corresponding formulas involving counts of permutation r…

Let $\mathbb{F}_q$ be a finite field, and let $N_{v,u}(q)$ denote the number of permutation rational functions $V(x)/U(x)$ over $\mathbb{F}_q$ with numerator degree $v$ and denomin…

Let $k$ be a positive integer, set $q=3^k$, and define … the set of $(q+1)$-th roots of unity in ${\mathbb F}_{q^2}$. A rational function permutes $\mu_{q+1}$ if it is defined on t…