The maximal generalised roundness of finite metric spaces

Abstract

A useful tool for computing the maximal generalised roundness of a finite metric space is a formula of Sánchez. Using well-known properties of the classical Cayley-Menger and Gramian matrices, we provide two simplifications of Sánchez’s formula that in particular do not require the calculation of any matrix inverses. To demonstrate the usefulness of these two new formulas we provide a simpler proof of Murugan’s classification of the subsets of the Hamming cube that have maximal generalised roundness greater than 1 1 .