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17983 Permuting Operations on Strings and Their Relation to Prime Numbers
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Asveld, P.R.J. (2010) Permuting Operations on Strings and Their Relation to Prime Numbers. Technical Report TR-CTIT-10-22, Centre for Telematics and Information Technology University of Twente, Enschede. ISSN 1381-3625

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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.

Item Type:Internal Report (Technical Report)
Research Group:EWI-HMI: Human Media Interaction
Uncontrolled Keywords:operation on strings, shuffle, twist, prime number, Josephus problem, Queneau number.
ID Code:17983
Deposited On:08 August 2011
International:No
More Information:statisticsmetis

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