### Abstract

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

Place of Publication | Enschede |

Publisher | Human Media Interaction (HMI) |

Number of pages | 46 |

Publication status | Published - 30 Jun 2009 |

### Publication series

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

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

No. | TR-CTIT-09-26 |

ISSN (Print) | 1381-3625 |

### Keywords

- Josephus problem
- Shuffle
- permutation
- Operation on strings
- cyclic subgroup
- EWI-15655
- distribution of prime numbers
- prime number
- MSC-68R15
- HMI-SLT: Speech and Language Technology
- MSC-11A07
- Twist
- IR-67513
- MSC-11A41
- METIS-263904

### Cite this

*Permuting Operations on Strings: Their Permutations and Their Primes*. (CTIT Technical Report Series; No. TR-CTIT-09-26). Enschede: Human Media Interaction (HMI).

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*Permuting Operations on Strings: Their Permutations and Their Primes*. CTIT Technical Report Series, no. TR-CTIT-09-26, Human Media Interaction (HMI), Enschede.

**Permuting Operations on Strings: Their Permutations and Their Primes.** / Asveld, P.R.J.

Research output: Book/Report › Report › Professional

TY - BOOK

T1 - Permuting Operations on Strings: Their Permutations and Their Primes

AU - Asveld, P.R.J.

N1 - eemcs-eprint-15655

PY - 2009/6/30

Y1 - 2009/6/30

N2 - We study some length-preserving operations on strings that permute the symbol positions in strings. These operations include some well-known examples (reversal, circular or cyclic shift, shuffle, twist, operations induced by the Josephus problem) and some new ones based on the Archimedes spiral. Such a permuting 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 such a permutation $X_n$. We call an integer $n$ $X$-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.

AB - We study some length-preserving operations on strings that permute the symbol positions in strings. These operations include some well-known examples (reversal, circular or cyclic shift, shuffle, twist, operations induced by the Josephus problem) and some new ones based on the Archimedes spiral. Such a permuting 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 such a permutation $X_n$. We call an integer $n$ $X$-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.

KW - Josephus problem

KW - Shuffle

KW - permutation

KW - Operation on strings

KW - cyclic subgroup

KW - EWI-15655

KW - distribution of prime numbers

KW - prime number

KW - MSC-68R15

KW - HMI-SLT: Speech and Language Technology

KW - MSC-11A07

KW - Twist

KW - IR-67513

KW - MSC-11A41

KW - METIS-263904

M3 - Report

T3 - CTIT Technical Report Series

BT - Permuting Operations on Strings: Their Permutations and Their Primes

PB - Human Media Interaction (HMI)

CY - Enschede

ER -