3 problems

Let $n$ be a positive integer and let $\pi\in\mathfrak{S}_n$ be a permutation of $\{1,\ldots,n\}$. Cyclic squared-difference conjecture. If $n>11$, there is a permutation $\pi$ suc…

Let $n$ be a positive integer and let $\pi\in\mathfrak{S}_n$ be a permutation of $\{1,\ldots,n\}$. Sun's squared-difference conjecture. If $n>7$, there is a permutation $\pi$ such…

Let $n$ be a positive integer and let $\pi\in\mathfrak{S}_n$ be a permutation of $\{1,\ldots,n\}$. Sun's reciprocal-sum conjecture. If $n>6$, there is a permutation $\pi$ such that…