MathOverflow

Consider the universe $U = \{1,2,\dots,n\}$. We uniformly sample $S\subseteq U, |S|=k$, and want to compute the probability of $S$ containing all of $1,2,\dots,d$ for a constant $d \le k$.
This is easily seen to be $\frac{\binom{n-d}{k-d}}{\binom nk}$ (number of good $S$ over total number of $S$), as well as $\frac{\binom kd}{\binom nd}$ (number of covered $d$-element sets by $S$ over total number of $d$-element sets)....

I wanted to know what the relation is between the KS-statistic an the TVD for two random variables $X$ and $Y$. but have not been able to find any clear description of this. I have only found one results that said that the total variation distance and...

By the twin prime conjecture, there are infinitely many primes of the form $p+2$, a sum of a prime and a primorial. In the opposite direction, one might ask If there are infinitely many primes that cannot be written as the sum of a prime and a primorial...

Let $d\in\mathbb{N}$, $s,t\in\mathbb{R}$ and $p,q\in [1,\infty]$. The Bessel operator is defined as$$ \mathcal{J}^s f = (I-\Delta)^{s/2}= \mathcal{F}^{-1}((1+|\cdot|^2)^{s/2}\mathcal{F}f)$$and the Bessel potential space is defined as$$ H^{s,p} = \mathcal...