A problem on distance matrices of subsets of the Hamming cube
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- by Ian Doust and Reinhard Wolf HTML | PDF
- Proc. Amer. Math. Soc. Ser. B 9 (2022), 125-134
Abstract:
Let $D$ denote the distance matrix for an $n+1$ point metric space $(X,d)$. In the case that $X$ is an unweighted metric tree, the sum of the entries in $D^{-1}$ is always equal to $2/n$. Such trees can be considered as affinely independent subsets of the Hamming cube $H_n$, and it was conjectured that the value $2/n$ was minimal among all such subsets. In this paper we confirm this conjecture and give a geometric interpretation of our result which applies to any subset of $H_n$.References
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Additional Information
- Ian Doust
- Affiliation: School of Mathematics and Statistics, UNSW Sydney, NSW 2052, Australia
- MR Author ID: 252035
- ORCID: 0000-0002-4694-9364
- Email: i.doust@unsw.edu.au
- Reinhard Wolf
- Affiliation: Institut für Mathematik, Universität Salzburg, Hellbrunnerstrasse 34, A-5020 Salzburg, Austria
- MR Author ID: 329171
- Email: Reinhard.Wolf@sbg.ac.at
- Received by editor(s): September 14, 2021
- Received by editor(s) in revised form: January 24, 2022
- Published electronically: April 8, 2022
- Communicated by: Stephen Dilworth
- © Copyright 2022 by the authors under Creative Commons Attribution 3.0 License (CC BY 3.0)
- Journal: Proc. Amer. Math. Soc. Ser. B 9 (2022), 125-134
- MSC (2020): Primary 46B85; Secondary 15A45, 51K99
- DOI: https://doi.org/10.1090/bproc/122
- MathSciNet review: 4405507