7 problems

Grunbaum–Yaakobi conjecture. Among all fair mechanisms on fixed parameters $(n,ell)$, the full model maximizes the expected coverage time.

There are $N$ coupon types, with draws made independently according to a probability vector $\mathbf{p}=(p_1,\ldots,p_N)$ in the open simplex … and let $T_N$ be the first time ever…

Let $P_{\mathcal{M}}$ be a stationary distribution with entropy $H$, let $H_N$ denote the LAWS hit rate after $N$ total queries, and let $N_{\min}$ be the per-node visit threshold.…

Finite variance extremality. The equal-probability vector $\nu$ minimizes

Let $Q_I(n,k)$ and $Q_{II}(n,k)$ denote the numbers of groups required to determine all coupon labels when the label set is known in advance and when it is not, respectively. For…

Let the universe consist of $n$ coupons, and let $H_t$ be an $r$-subset drawn at round $t$. Starting from $H_t$, form $H_{t+1}$ by choosing a uniformly random coupon in $H_t$ and r…

Let $n\geq 1$, let $c\in\{1,\ldots,n\}$, and let $p=(p_1,\ldots,p_n)\in(0,1)^n$ satisfy $p_1+\cdots+p_n\leq 1$. Write … Here $T_{c,n}(p)$ denotes the time needed in the generalized…