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15655 Permuting Operations on Strings: Their Permutations and Their Primes
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Asveld, P.R.J. (2009) Permuting Operations on Strings: Their Permutations and Their Primes. Technical Report TR-CTIT-09-26, Centre for Telematics and Information Technology, University of Twente, Enschede. ISSN 1381-3625

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Abstract

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 Archimedes spiral. Such a permuting operation $X$ gives rise to a family $\{p(X,n)\}_{n\geq2}$ of similar permutations. We investigate the structure and the order of the cyclic group generated by such a permutation $p(X,n)$. We call an integer $n$ $X$-prime if $p(X,n)$ 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.

Item Type:Internal Report (Technical Report)
Research Group:EWI-HMI: Human Media Interaction
Uncontrolled Keywords:operation on strings, shuffle, twist, permutation, cyclic subgroup, prime number, Josephus problem, distribution of prime numbers
ID Code:15655
Deposited By:P.R.J. Asveld
Deposited On:22 September 2009
International:No
More Information:statisticsmetis

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