A PROBLEM ON DISTANCE MATRICES OF SUBSETS OF THE HAMMING CUBE
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 Hn, and it was conjectured that the value 2...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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American Mathematical Society
2022
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| Online Access: | View Fulltext in Publisher |
| Summary: | 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 Hn, 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 Hn. © 2022, American Mathematical Society. All rights reserved. |
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| ISBN: | 23301511 (ISSN) |
| DOI: | 10.1090/bproc/122 |