# Permuting Operations on Strings: Their Permutations and Their Primes

P.R.J. Asveld

Research output: Book/ReportReportProfessional

## Abstract

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.
Original language Undefined Enschede Centre for Telematics and Information Technology (CTIT) 46 Published - 30 Jun 2009

### Publication series

Name CTIT Technical Report Series University of Twente, Centre for Telematica and Information Technology (CTIT) TR-CTIT-09-26 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