6 problems

Exponent reduction conjecture. The exponent $\frac{n(n+1)}{2}-1$ can be reduced to $\frac{n(n-1)}{2}$.

Linear lower-bound conjecture. The minimal number satisfies

Afkhami-Jeddi–Cohn–Hartman–de Laat–Tajdini conjecture. The current linear-programming methods should attain the bound

For fixed $k\ge 2$ and $\lambda>0$, let $m_{k,\lambda}$ denote the mode of the Poisson distribution of order $k$. The constants $c_0$ and $c_1$ are to be determined. Improved lower…

Let \text{mathsf{CAN}}_\lambda(t,k,v) denote the smallest number of rows in a covering array with strength $t$, $k$ columns, alphabet size $v$, and covering multiplicity…

Let $q>2$ and let $\theta=1-1/q$. For $x$ in the relevant relative-distance range, write $\alpha(x)=\lim_{n\to\infty}n^{-1}\log_q A_q(n,xn)$, where $A_q(n,d)$ is the maximum size o…