Permuting Operations on Strings and the Distribution of Their Prime Numbers

P.R.J. Asveld

Research output: Book/ReportReportProfessional

53 Downloads (Pure)

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 languageUndefined
Place of PublicationEnschede
PublisherCentre for Telematics and Information Technology (CTIT)
Number of pages22
Publication statusPublished - 17 Oct 2011

Publication series

NameCTIT Technical Report Series
PublisherUniversity of Twente, Centre for Telematics and Information Technology
No.TR-CTIT-11-24
ISSN (Print)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).
Asveld, P.R.J. / Permuting Operations on Strings and the Distribution of Their Prime Numbers. Enschede : Centre for Telematics and Information Technology (CTIT), 2011. 22 p. (CTIT Technical Report Series; TR-CTIT-11-24).
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Asveld, PRJ 2011, Permuting Operations on Strings and the Distribution of Their Prime Numbers. CTIT Technical Report Series, no. TR-CTIT-11-24, Centre for Telematics and Information Technology (CTIT), Enschede.

Permuting Operations on Strings and the Distribution of Their Prime Numbers. / Asveld, P.R.J.

Enschede : Centre for Telematics and Information Technology (CTIT), 2011. 22 p. (CTIT Technical Report Series; No. TR-CTIT-11-24).

Research output: Book/ReportReportProfessional

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AB - 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.

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Asveld PRJ. Permuting Operations on Strings and the Distribution of Their Prime Numbers. Enschede: Centre for Telematics and Information Technology (CTIT), 2011. 22 p. (CTIT Technical Report Series; TR-CTIT-11-24).