# Permuting Operations on Strings and the Distribution of Their Prime Numbers

Asveld, Peter R.J. (2011) *Permuting Operations on Strings and the Distribution of Their Prime Numbers.* [Report]

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Abstract: | Several ways of interleaving, as studied in theoretical computer science, and some subjects from mathematics can be modeled by length-preserving operations on strings, that only permute the symbol positions in strings. Each such operation X gives rise to a family n≥2} of similar permutations. We call an integer n X-prime if Xn consists of a single cycle of length n(n≥2). For some instances of X - such as shuffle, twist, operations based on the Archimedes' spiral and on the Josephus problem - we investigate the distribution of X-primes and of the associated (ordinary) prime numbers, which leads to variations of some well-known conjectures in number theory. [brace not closed] |

Item Type: | Report |

Faculty: | Electrical Engineering, Mathematics and Computer Science (EEMCS) |

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Link to this item: | http://purl.utwente.nl/publications/78281 |

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Metis ID: 278873