Münchhausen Matrices
"The Baron's omni-sequence", $B(n)$, first defined by Khovanova and Lewis (2011), is a sequence that gives for each $n$ the minimum number of weighings on balance scales that can verify the correct labeling of $n$ identically-looking coins with distinct integer weights between $1$ gram and $n$ grams.A trivial lower bound on $B(n)$ is $\log_3 n$, and it has been shown that $B(n)$ is $\text{O}(\log n)$.We introduce new theoretical tools for the study of this problem, and show that $B(n)$ is $\log_3 n + \text{O}(\log \log n)$, thus settling in the affirmative a conjecture by Khovanova and Lewis that the true growth rate of the sequence is very close to the natural lower bound.
2014 ◽
Vol 24
(4)
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pp. 658-679
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2004 ◽
Vol 14
(05n06)
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pp. 677-702
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2020 ◽
Vol 29
(04)
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pp. 2050022
1997 ◽
Vol 6
(3)
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pp. 353-358
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2008 ◽
Vol Vol. 10 no. 3
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2005 ◽
Vol DMTCS Proceedings vol. AE,...
(Proceedings)
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2010 ◽
Vol 19
(11)
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pp. 1449-1456
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