### 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 $\{X_n\}_{n\geq2}$ of similar permutations. We call an integer $n$ $X$-{\em prime} if $X_n$ consists of a single cycle of length $n$ ($n\geq2$). 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.

Original language | Undefined |
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Place of Publication | Enschede |

Publisher | Centre for Telematics and Information Technology (CTIT) |

Number of pages | 22 |

Publication status | Published - 17 Oct 2011 |

### Publication series

Name | CTIT Technical Report Series |
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Publisher | University of Twente, Centre for Telematics and Information Technology |

No. | TR-CTIT-11-24 |

ISSN (Print) | 1381-3625 |

### Keywords

- MSC-68R15
- EWI-20685
- distribution of prime numbers
- Shuffle
- Josephus problem
- Queneau number
- Twist
- Artin's conjecture (on primitive roots)
- Archimedes' spiral
- IR-78281
- METIS-278873
- MSC-11B25
- MSC-11A41
- MSC-11A07
- HMI-SLT: Speech and Language Technology

## Cite this

Asveld, P. R. J. (2011).

*Permuting Operations on Strings and the Distribution of Their Prime Numbers*. (CTIT Technical Report Series; No. TR-CTIT-11-24). Enschede: Centre for Telematics and Information Technology (CTIT).