The maximal generalised roundness of finite metric spaces

Robertson, Gavin

doi:10.1090/proc/15298

The maximal generalised roundness of finite metric spaces

Author: Gavin Robertson
Journal: Proc. Amer. Math. Soc. 149 (2021), 407-411
MSC (2020): Primary 52C99; Secondary 43A35
DOI: https://doi.org/10.1090/proc/15298
Published electronically: October 20, 2020
MathSciNet review: 4172615
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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 $1$.

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