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arXiv · 0804.1214

New Lower Bounds for the Maximum Number of Runs in a String

Kazuhiko Kusano·Wataru Matsubara·Akira Ishino·Hideo Bannai·Ayumi Shinohara
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Abstract

We show a new lower bound for the maximum number of runs in a string. We prove that for any e > 0, (a -- e)n is an asymptotic lower bound, where a = 56733/60064 = 0.944542. It is superior to the previous bound 0.927 given by Franek et al. Moreover, our construction of the strings and the proof is much simpler than theirs.

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Kazuhiko Kusano, Wataru Matsubara, Akira Ishino, Hideo Bannai, Ayumi Shinohara. 2008-04-08. New Lower Bounds for the Maximum Number of Runs in a String. https://arxiv.org/abs/0804.1214

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