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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The maximal generalised roundness of finite metric spaces
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by Gavin Robertson PDF
Proc. Amer. Math. Soc. 149 (2021), 407-411 Request permission


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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Additional Information
  • Gavin Robertson
  • Affiliation: School of Mathematics and Statistics, University of New South Wales, Sydney NSW 2052, Australia
  • ORCID: 0000-0003-4231-4879
  • Email:
  • 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
  • © Copyright 2020 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 149 (2021), 407-411
  • MSC (2020): Primary 52C99; Secondary 43A35
  • DOI:
  • MathSciNet review: 4172615