7 problems

A permutation array is an element $P$ of $[n]^d$ satisfying the permutation-array conditions, and $X^o_P$ denotes the corresponding permutation array variety, consisting of tuples…

The paper studies permutation arrays and introduces the quantities $c_r$ and $d_r$ in Theorem fixed; the preceding context does not specify their definitions or the exact bounds st…

Let an $(n,m,d)$-array be a set of strings of length $n$ over an alphabet of size $m$, with pairwise Kendall-$\tau$ distance at least $d$, and let $P(n,d)$ denote the relevant maxi…

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…

Partition-and-extension conjecture.

Existence conjecture. A type-$1,2,3,4$ LRPA$(n)$ exists for all positive integers $n$.