5 problems

Moment-determination conjecture. The phenomenon that the moments

Structure conjecture. If

Károlyi's inverse Erdős–Heilbronn conjecture. The equality

Let $G$ be a nonabelian group, and let $A$ and $B$ be subsets whose restricted product set consists of products $ab$ with the factors subject to the distinctness restriction. Károl…

Let $G$ be a locally compact group, let $A\subset G$ be a compact neighborhood, and let $\mu$ be Haar measure on $G$. For $n\geqslant 1$, write $A^n$ for the $n$-fold product set o…