### 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 $n$ {\em $X$-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 on the density of certain sets of prime numbers.

Original language | English |
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Pages (from-to) | 1868-1881 |

Number of pages | 14 |

Journal | Discrete applied mathematics |

Volume | 161 |

Issue number | 13-14 |

DOIs | |

Publication status | Published - Sep 2013 |

### Keywords

- HMI-SLT: Speech and Language Technology
- MSC-11A07
- MSC-11N05
- MSC-12E20
- distribution of prime numbers
- Artin's conjecture (on primitive roots)
- Archimedes' spiral
- Twist
- Queneau number
- Shuffle
- Josephus problem
- METIS-297691
- MSC-68R15

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## Cite this

Asveld, P. R. J. (2013). Permuting Operations on Strings and the Distribution of Their Prime Numbers.

*Discrete applied mathematics*,*161*(13-14), 1868-1881. https://doi.org/10.1016/j.dam.2013.03.002