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 log3 n, and it has been shown that B(n) is O(log n). We introduce new theoretical tools for the study of this problem, and show that B(n) is log3 n + 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.