Ferenc SZÖLLŐSI（Aalto University）「Towards the classification of few-distance sets」
Let $d$, $n$, and $s$ be positive integers, and let $R^d$ be the usual Euclidean space equipped with the standard Euclidean distance function $\mu$. An $n$-element set of (distinct) vectors $X$ in $R^d$ is called an $s$-distance set, if the cardinality of the set of distances $A(X):=\{\mu(X_i,X_j) : 0 < i < j < n+1\}$ is exactly $s$. In this talk I will present a combined approach of isomorph-free exhaustive generation of graphs and Grobner basis computation which results in the complete classification of the maximum $3$-distance sets in $R^4$ and the maximum $4$-distance sets in $R^3$.