### Abstract

Original language | Undefined |
---|---|

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 |
---|---|

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

*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).

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

**Permuting Operations on Strings and the Distribution of Their Prime Numbers.** / Asveld, P.R.J.

Research output: Book/Report › Report › Professional

TY - BOOK

T1 - Permuting Operations on Strings and the Distribution of Their Prime Numbers

AU - Asveld, P.R.J.

N1 - eemcs-eprint-20685

PY - 2011/10/17

Y1 - 2011/10/17

N2 - 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.

AB - 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.

KW - MSC-68R15

KW - EWI-20685

KW - distribution of prime numbers

KW - Shuffle

KW - Josephus problem

KW - Queneau number

KW - Twist

KW - Artin's conjecture (on primitive roots)

KW - Archimedes' spiral

KW - IR-78281

KW - METIS-278873

KW - MSC-11B25

KW - MSC-11A41

KW - MSC-11A07

KW - HMI-SLT: Speech and Language Technology

M3 - Report

T3 - CTIT Technical Report Series

BT - Permuting Operations on Strings and the Distribution of Their Prime Numbers

PB - Centre for Telematics and Information Technology (CTIT)

CY - Enschede

ER -