All Questions

Let $C^n=\{0,1\}^n$ be a metric space (Hamming Cube). The distance on $C^n$ is defined by $$ d(\varepsilon,\varepsilon'):=|\{j:\varepsilon_j\ne\varepsilon'_j\}|, $$ $\varepsilon=(\varepsilon_1,\...

We are given the sequence defined by the recurrence relation $a_{n+1}=a_n^2+1$ with $a_0=0$. Let $h$ be a positive integer (it represents the maximum number of bits, up to a constant factor, that we ...

Question: How can we prove that there exists a real constant $c\ge 1$ such that the following inequality holds for all integers $d>1$ and all real numbers $r\in\left[1,\sqrt{d}\right]$? $$\int_{-1}^...