The total run length of a word
Access Status
Authors
Date
2013Type
Metadata
Show full item recordAbstract
A run in a word is a periodic factor whose length is at least twice its period and which cannot be extended to the left or right (by a letter) to a factor with greater period. In recent years a great deal of work has been done on estimating the maximum number of runs that can occur in a word of length n. A number of associated problems have also been investigated. In this paper we consider a new variation on the theme. We say that the total run length (TRL) of a word is the sum of the lengths of the runs in the word and that τ(n) is the maximum TRL over all words of length n. We show that n2/8<τ(n)<47n2/72+2nn2/8<τ(n)<47n2/72+2n for all n. We also give a formula for the average total run length of words of length n over an alphabet of size α, and some other results.
Citation
Source Title
Remarks
NOTICE: this is the author’s version of a work that was accepted for publication in Theoretical Computer Science. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Theoretical Computer Science, Vol. 501(2013). DOI: 10.1016/j.tcs.2013.06.004
Collections
Related items
Showing items related by title, author, creator and subject.

Kong, Paul Y.L. (1993)Key words: End zone, prestress transfer, wire tendon, transmission length, pullin, plain wire, indented wire, concrete strength, size of wire, gradual release, sudden release, shock release, time dependent effects.An ...

Crochemore, M.; Iliopoulos, Costas; Kubica, M.; Kubica, M.; Radoszewski, J.; Rytter, W.; Walen, T. (2014)A breakthrough in the field of text algorithms was the discovery of the fact that the maximal number of runs in a word of length n is O(n) and that they can all be computed in O(n) time. We study some applications of this ...

Simpson, Jamie (2014)There is a very short and beautiful proof that the number of distinct nonempty palindromes in a word of length n is at most n. In this paper we show, with a very complicated proof, that the number of distinct nonempty ...