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20685 Permuting Operations on Strings and the Distribution of Their Prime Numbers
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Asveld, P.R.J. (2011) Permuting Operations on Strings and the Distribution of Their Prime Numbers. Technical Report TR-CTIT-11-24, Centre for Telematics and Information Technology University of Twente, Enschede. ISSN 1381-3625

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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.

Item Type:Internal Report (Technical Report)
Research Group:EWI-HMI: Human Media Interaction
Uncontrolled Keywords:Shuffle, twist, Archimedes' spiral, Josephus problem, Queneau number, distribution of prime numbers, Artin's conjecture (on primitive roots)
ID Code:20685
Deposited On:18 October 2011
International:No
More Information:statisticsmetis

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