# Permuting Operations on Strings and Their Relation to Prime Numbers

P.R.J. Asveld

Research output: Book/ReportReportProfessional

### Abstract

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.
Original language Undefined Enschede Centre for Telematics and Information Technology (CTIT) 24 Published - 7 Jun 2010

### Publication series

Name CTIT Technical Report Series University of Twente, Centre for Telematica and Information Technology (CTIT) TR-CTIT-10-22 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

Asveld, P. R. J. (2010). 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).