7 problems

Let $k$ and $t$ be fixed, and let $D=\binom{k}{t}-1$. Consider a covering produced by the random greedy algorithm, and define its density as the number of blocks divided by the asy…

Explicit asymptotic formula conjecture. If $d$ is odd and

Linear-growth conjecture. For all fixed $d$ and $k$, there exists a constant $C_{d,k}$ such that

Three-dimensional covering conjecture. For all $n,k\geq 1$,

Two-dimensional asymptotic conjecture. For all positive integers $n$ and $k$,

Let $n$ be an odd positive integer, and let $\xi(n)$ denote the toroidal covering parameter. Multiplicative reduction conjecture. … This conjecture proposes an exact reduction of t…

Let $S_n$ be the set of permutations of $\{1,\ldots,n\}$, and let $\kappa_n$ denote the minimum number of $(n+1)$-permutations needed to cover every $n$-permutation. Asymptotic cov…