3 problems

Let $m=\Omega(n)$ balls be allocated to $n$ bins in the two-thinning setting, and let the overseer two-thin the allocations. More-balls conjecture. The asymptotically optimal maxim…

Let $n$ bins receive balls in the two-thinning setting, where the overseer may iteratively reject up to $k$ suggested allocations for each ball. More-choice conjecture. The asympto…

Storage-efficiency conjecture. If $l=2$ and $q-1=c\ln n$, then the load-balancing modulation code has storage efficiency $\gamma=k$ with probability $1-o(1)$ as…