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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
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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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Gavin Robertson
Affiliation: School of Mathematics and Statistics, University of New South Wales, Sydney NSW 2052, Australia
Email: gavin.robertson@unsw.edu.au

DOI: https://doi.org/10.1090/proc/15298
Received by editor(s): April 22, 2020
Received by editor(s) in revised form: July 19, 2020, and July 21, 2020
Published electronically: October 20, 2020
Communicated by: Stephen Dilworth
Article copyright: © Copyright 2020 American Mathematical Society