The maximal number of cubic runs in a word

Authors:
M. Crochemore;C. S. Iliopoulos;M. Kubica;J. Radoszewski;W. Rytter;T. Waleń
Affiliations:
Kings College London, London WC2R 2LS, UK and Université Paris-Est, France;Kings College London, London WC2R 2LS, UK and Digital Ecosystems & Business Intelligence Institute, Curtin University of Technology, Perth, WA 6845, Australia;Dept. of Mathematics, Informatics and Mechanics, University of Warsaw, ul. Banacha 2, 02-097 Warsaw, Poland;Dept. of Mathematics, Informatics and Mechanics, University of Warsaw, ul. Banacha 2, 02-097 Warsaw, Poland;Dept. of Mathematics, Informatics and Mechanics, University of Warsaw, ul. Banacha 2, 02-097 Warsaw, Poland and Dept. of Math. and Informatics, Copernicus University, ul. Chopina 12/18, 87-100 Tor ...;Dept. of Mathematics, Informatics and Mechanics, University of Warsaw, ul. Banacha 2, 02-097 Warsaw, Poland
Venue:
Journal of Computer and System Sciences
Year:
2012

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Abstract

A run is an inclusion maximal occurrence in a word (as a subinterval) of a factor in which the period repeats at least twice. The maximal number of runs in a word of length n has been thoroughly studied, and is known to be between 0.944n and 1.029n. The proofs are very technical. In this paper we investigate cubic runs, in which the period repeats at least three times. We show the upper bound on their maximal number, cubic-runs(n), in a word of length n: cubic-runs(n)