# Permuting Operations on Strings and the Distribution of Their Prime Numbers

P.R.J. Asveld

Research output: Book/ReportReportProfessional

### Abstract

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.
Original language Undefined Enschede Centre for Telematics and Information Technology (CTIT) 22 Published - 17 Oct 2011

### Publication series

Name CTIT Technical Report Series University of Twente, Centre for Telematics and Information Technology TR-CTIT-11-24 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

Asveld, P. R. J. (2011). 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).