2 problems

Let $m$ be a positive integer, let $w\in\mathbb{R}_{>0}^m$ satisfy … and let $v\in\{0,1\}^m$ have independent Bernoulli$(p)$ coordinates, where $0\leq p\leq 1/3$. Weighted Bernoull…

Csóka's conjecture. For every $p$ and $t$ there exists a $k\in\mathbb N$ such that $\pi(p,t)$ is realized by $c_i=\frac1k$ for $i\leq k$ and $c_i=0$ for $i>k$; equivalently, the ma…