On k-diametral point configurations in Minkowski spaces

The structure of k-diametral point configurations in Minkowski d-space is shown to be closely related to the properties of k-antipodal point configurations in Rd. In particular, the maximum size of k-diametral point configurations of Minkowski d-spaces is obtained for given k >= 2 and d >= 2 generalizing Petty's results (Petty, 1971 [24]) on equilateral sets in Minkowski spaces. Furthermore, bounds are derived for the maximum size of k-diametral point configurations in given Minkowski d-space (resp., Euclidean d-space). Some of these results have analogues for point sets, which are discussed as well. In the proofs convexity methods are combined with volumetric estimates and combinatorial properties of diameter graphs. (C) 2021 Elsevier B.V. All rights reserved.