The maximal number of cubic runs in a word

The maximal number of cubic runs in a word

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 in...

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Veröffentlicht in:Journal of computer and system sciences 2012-11, Vol.78 (6), p.1828-1836
Hauptverfasser: Crochemore, M., Iliopoulos, C.S., Kubica, M., Radoszewski, J., Rytter, W., Waleń, T.
Format: Artikel
Sprache:eng
Schlagworte:
Alphabets
Combinatorics
Computer Science
Construction
Data Structures and Algorithms
Fibonacci word
Inclusions
Linearity
Lower bounds
Lyndon word
Mathematics
Proving
Run in a word
Upper bounds
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Beschreibung
Zusammenfassung: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)
ISSN:0022-0000
1090-2724
DOI:10.1016/j.jcss.2011.12.005