4 problems

Let $-1 \leq \beta < 0 \leq \alpha < 1$. A spherical two-distance set in $\mathbb{R}^d$ is a collection of unit vectors whose pairwise inner products lie in $\{\alpha,\beta\}$. Let…

Let $N_{[-1,\beta]\cup\{\alpha_1,\dots,\alpha_k\}}(d)$ denote the maximum size of a spherical two-distance set in $\mathbb R^d$ whose inner products lie in…

Fix $-1\le\beta<0\le\alpha<1$. For a spherical two-distance set in $\mathbb R^d$ with inner products in $\{\alpha,\beta\}$, let $N_{\alpha,\beta}(d)$ be the maximum possible size.…

Let $g(n)$ denote the maximum cardinality of a spherical two-distance set in $\mathbb{R}^n$. Maximum spherical two-distance set conjecture. … The conjecture reflects the observed p…