6 problems

Let $B_{n,k}(p)$ be the binomial tail probability, $b_{n,k}(p)$ the corresponding binomial point probability, and $L(n,k,p)$ the lower bound from the paper's Theorem. Suppose…

Binomial $(S_2)$ conjecture. $X$ satisfies Condition $(S_2)$.

Chvátal's inverse-unimodality conjecture. The sequence $(q_m)_{m=0}^n$ is inverse unimodal for all $n$.

Let $ctilde\xi_{b,n}\sim\operatorname{Bin}(n,b/(n+1))$, and define … For $X=(\alpha,\beta)\in(0,1)\times(1,\infty)$ and an integer $b$ satisfying … let $cxi_1,\ldots,\xi_n$ be inde…

Let $p$ denote the parameter in the binomial distribution, and let Inequality … can be significantly improved when $p=\frac{1}{2}$. This conjecture motivated the research in the pa…

The sharpened Tusnády inequality. The bounds