Permuting operations on strings and their relation to prime numbers Original Research Article

Some length-preserving operations on strings only permute the symbol positions in strings; such an operation image gives rise to a family image of similar permutations. We investigate the structure and the order of the cyclic group generated by image. We call an integer image image-prime if image consists of a single cycle of length image (image). Then we show some properties of these image-primes, particularly, how image-primes are related to image-primes as well as to ordinary prime numbers. Here image and image range over well-known examples (reversal, cyclic shift, shuffle, twist) and some new ones based on the Archimedes spiral and on the Josephus problem.