Hierarchies of Principal Twist-Closed Trios
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
Refining the hierarchy of blind multicounter languages and twist-closed trios
Information and Computation
Generating all permutations by context-free grammars in Chomsky normal form
Theoretical Computer Science - Algebraic methods in language processing
Generating all permutations by context-free grammars in Greibach normal form
Theoretical Computer Science
Fundamental Number Theory with Applications, Second Edition
Fundamental Number Theory with Applications, Second Edition
Generating all circular shifts by context-free grammars in Chomsky normal form
Journal of Automata, Languages and Combinatorics
Permuting operations on strings and the distribution of their prime numbers
Discrete Applied Mathematics
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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"="2 of similar permutations. We investigate the structure and the order of the cyclic group generated by X"n. We call an integer n X-prime if X"n consists of a single cycle of length n (n=2). Then we show some properties of these X-primes, particularly, how X-primes are related to X^'-primes as well as to ordinary prime numbers. Here X and X^' range over well-known examples (reversal, cyclic shift, shuffle, twist) and some new ones based on the Archimedes spiral and on the Josephus problem.