Permuting Operations on Strings and Their Relation to Prime Numbers

P.R.J. Asveld

Research output: Book/ReportReportProfessional

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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 languageUndefined
Place of PublicationEnschede
PublisherCentre for Telematics and Information Technology (CTIT)
Number of pages24
Publication statusPublished - 7 Jun 2010

Publication series

NameCTIT Technical Report Series
PublisherUniversity of Twente, Centre for Telematica and Information Technology (CTIT)
No.TR-CTIT-10-22
ISSN (Print)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).
Asveld, P.R.J. / Permuting Operations on Strings and Their Relation to Prime Numbers. Enschede : Centre for Telematics and Information Technology (CTIT), 2010. 24 p. (CTIT Technical Report Series; TR-CTIT-10-22).
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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.",
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Asveld, PRJ 2010, Permuting Operations on Strings and Their Relation to Prime Numbers. CTIT Technical Report Series, no. TR-CTIT-10-22, Centre for Telematics and Information Technology (CTIT), Enschede.

Permuting Operations on Strings and Their Relation to Prime Numbers. / Asveld, P.R.J.

Enschede : Centre for Telematics and Information Technology (CTIT), 2010. 24 p. (CTIT Technical Report Series; No. TR-CTIT-10-22).

Research output: Book/ReportReportProfessional

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AB - 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.

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Asveld PRJ. Permuting Operations on Strings and Their Relation to Prime Numbers. Enschede: Centre for Telematics and Information Technology (CTIT), 2010. 24 p. (CTIT Technical Report Series; TR-CTIT-10-22).