## Abstract

Two strings u and v are said to be Abelian equivalent if u is a permutation of the characters of v. We introduce two new regularities on strings w.r.t. Abelian equivalence, called Abelian covers and Abelian runs, which are generalizations of covers and runs of strings, respectively. We show how to determine in O(n) time whether or not a given string w of length n has an Abelian cover. Also, we show how to compute an O(n^{2})-size representation of (possibly exponentially many) Abelian covers of w in O(n^{2}) time. Moreover, we present how to compute all Abelian runs in w in O(n^{2}) time, and state that the maximum number of all Abelian runs in a string of length n is Ω(n^{2}).

Original language | English |
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Title of host publication | Proceedings of the Prague Stringology Conference 2014, PSC 2014 |

Publisher | Prague Stringology Club |

Pages | 43-51 |

Number of pages | 9 |

ISBN (Electronic) | 9788001055472 |

Publication status | Published - 2014 |

Event | 18th Prague Stringology Conference, PSC 2014 - Prague, Czech Republic Duration: Sept 1 2014 → Sept 3 2014 |

### Other

Other | 18th Prague Stringology Conference, PSC 2014 |
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Country/Territory | Czech Republic |

City | Prague |

Period | 9/1/14 → 9/3/14 |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)