### Abstract

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

Place of Publication | Enschede |

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

Number of pages | 24 |

Publication status | Published - 7 Jun 2010 |

### Publication series

Name | CTIT Technical Report Series |
---|---|

Publisher | University of Twente, Centre for Telematica and Information Technology (CTIT) |

No. | TR-CTIT-10-22 |

ISSN (Print) | 1381-3625 |

### Keywords

- Operation on strings
- MSC-11A41
- Josephus problem
- Queneau number
- Twist
- IR-71704
- METIS-270843
- Shuffle
- MSC-11A07
- HMI-SLT: Speech and Language Technology
- MSC-68R15
- prime number
- EWI-17983

### Cite this

*Permuting Operations on Strings and Their Relation to Prime Numbers*. (CTIT Technical Report Series; No. TR-CTIT-10-22). Enschede: Centre for Telematics and Information Technology (CTIT).

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*Permuting Operations on Strings and Their Relation to Prime Numbers*. CTIT Technical Report Series, no. TR-CTIT-10-22, Centre for Telematics and Information Technology (CTIT), Enschede.

**Permuting Operations on Strings and Their Relation to Prime Numbers.** / Asveld, P.R.J.

Research output: Book/Report › Report › Professional

TY - BOOK

T1 - Permuting Operations on Strings and Their Relation to Prime Numbers

AU - Asveld, P.R.J.

N1 - eemcs-eprint-17983

PY - 2010/6/7

Y1 - 2010/6/7

N2 - Some length-preserving operations on strings only permute the symbol positions in strings; such an operation $X$ gives rise to a family $\{X_n\}_{n\geq2}$ of similar permutations. We investigate the structure and the order of the cyclic group generated by $X_n$. We call an integer $n$ $X$-{\em prime} if $X_n$ consists of a single cycle of length $n$ ($n\geq2$). Then we show some properties of these $X$-primes, particularly, how $X$-primes are related to $X^\prime$-primes as well as to ordinary prime numbers. Here $X$ and $X^\prime$ range over well-known examples (reversal, cyclic shift, shuffle, twist) and some new ones based on the Archimedes spiral and on the Josephus problem.

AB - Some length-preserving operations on strings only permute the symbol positions in strings; such an operation $X$ gives rise to a family $\{X_n\}_{n\geq2}$ of similar permutations. We investigate the structure and the order of the cyclic group generated by $X_n$. We call an integer $n$ $X$-{\em prime} if $X_n$ consists of a single cycle of length $n$ ($n\geq2$). Then we show some properties of these $X$-primes, particularly, how $X$-primes are related to $X^\prime$-primes as well as to ordinary prime numbers. Here $X$ and $X^\prime$ range over well-known examples (reversal, cyclic shift, shuffle, twist) and some new ones based on the Archimedes spiral and on the Josephus problem.

KW - Operation on strings

KW - MSC-11A41

KW - Josephus problem

KW - Queneau number

KW - Twist

KW - IR-71704

KW - METIS-270843

KW - Shuffle

KW - MSC-11A07

KW - HMI-SLT: Speech and Language Technology

KW - MSC-68R15

KW - prime number

KW - EWI-17983

M3 - Report

T3 - CTIT Technical Report Series

BT - Permuting Operations on Strings and Their Relation to Prime Numbers

PB - Centre for Telematics and Information Technology (CTIT)

CY - Enschede

ER -