A Series of Run-Rich Strings

Authors:
Wataru Matsubara;Kazuhiko Kusano;Hideo Bannai;Ayumi Shinohara
Affiliations:
Graduate School of Information Science, Tohoku University, Sendai, Japan 980-8579;Graduate School of Information Science, Tohoku University, Sendai, Japan 980-8579;Department of Informatics, Kyushu University, Fukuoka, Japan 819-0395;Graduate School of Information Science, Tohoku University, Sendai, Japan 980-8579
Venue:
LATA '09 Proceedings of the 3rd International Conference on Language and Automata Theory and Applications
Year:
2009

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Abstract

We present a new series of run-rich strings, and give a new lower bound 0.94457567 of the maximum number of runs in a string. We also introduce the general conjecture about a asymptotic behavior of the numbers of runs in the strings defined by any recurrence formula, and show the lower bound can be improved further to 0.94457571235.