Permuting Operations on Strings: Their Permutations and Their Primes

P.R.J. Asveld

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    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 languageUndefined
    Place of PublicationEnschede
    PublisherCentre for Telematics and Information Technology (CTIT)
    Number of pages46
    Publication statusPublished - 30 Jun 2009

    Publication series

    NameCTIT Technical Report Series
    PublisherUniversity of Twente, Centre for Telematica and Information Technology (CTIT)
    ISSN (Print)1381-3625


    • 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

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