### Abstract

A substring w[i.j] in w is called a repetition of period p if s[k] = s[k + p] for any i ≤ k ≤ j - p. Especially, a maximal repetition, which cannot be extended neither to left nor to right, is called a run. The ratio of the length of the run to its period, i.e. j-i+1/p, is called an exponent. The sum of exponents of runs in a string is of interest. The maximal value of the sum is still unknown, and the current upper bound is 2.9n given by Crochemore and Ilie, where n is the length of a string. In this paper we show a closed formula which exactly expresses the average value of it for any n and any alphabet size, and the limit of this value per unit length as n approaches infinity. For binary strings, the limit value is approximately 1.13103.

Original language | English |
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Title of host publication | Proceedings of the Prague Stringology Conference 2008 |

Pages | 185-192 |

Number of pages | 8 |

Publication status | Published - 2008 Dec 1 |

Event | Prague Stringology Conference 2008, PSC 2008 - Prague, Czech Republic Duration: 2008 Sep 1 → 2008 Sep 3 |

### Publication series

Name | Proceedings of the Prague Stringology Conference 2008 |
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### Other

Other | Prague Stringology Conference 2008, PSC 2008 |
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Country | Czech Republic |

City | Prague |

Period | 08/9/1 → 08/9/3 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

*Proceedings of the Prague Stringology Conference 2008*(pp. 185-192). (Proceedings of the Prague Stringology Conference 2008).