3 problems

Let $\mathrm{DIAM}(d,k,n)$ be the maximum number of unit $k$-simplices spanned by an $n$-point set in $\mathbb{R}^d$ of diameter $1$. Conjecture on unit simplices in diameter graph…

Let $S_1$ and $S_2$ be two unit simplices in $\mathbb R^d$ forming a set of diameter $1$, with $k$ and $m$ vertices respectively, and assume $k\geq m$. Schur's conjecture. The simp…

Let an almost-equidistant diameter set be a set of points in $\mathbb R^d$ of diameter $1$ in which every three points contain a pair at distance $1$. The extremal bound conjecture…