Proof of a conjecture by Walter Deuber concerning the distances between points of two types in \(R^d\)
The author proves Deuber's conjecture [Problem 303 in \textit{W. Deuber}, Discrete Math. 192, 348 (1998)]: For equal numbers of black and white points in Euclidean space the sum of the pairwise distances between points of equal colour is less than or equal to the sum of the pairwise distances between points of different colour, and equality holds only in the case when black and white points coincide. This is proved by simple counting and application of a well-known fact from integral geometry.
scientific article; zbMATH DE number 1565950