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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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Some length-preserving operations on strings only permute the symbol positions in strings; such an operation gives rise to a family of similar permutations. We investigate the structure and the order of the cyclic group generated by . We call an integer - if consists of a single cycle of length (). Then we show some properties of these -primes, particularly, how -primes are related to -primes as well as to ordinary prime numbers. Here and 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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