Average number of occurrences of repetitions in a necklace

Kazuhiko Kusano, Ayumi Shinohara

Research output: Contribution to journalArticlepeer-review


In this paper, we consider the average number of occurrences of primitively rooted repetitions in a necklace. First, we define circular repetitions for a string and show the average number of them. Using these results, we can obtain the average number of squares, cubes, runs and cubic runs and the average sum of exponents of runs and cubic runs in a necklace, exactly.

Original languageEnglish
Pages (from-to)334-342
Number of pages9
JournalDiscrete Applied Mathematics
Issue numberPART 3
Publication statusPublished - 2014 Jan 30


  • Combinatorics on words
  • Repetition
  • Run

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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