Permuting operations on strings and their relation to prime numbers


Asveld, Peter R.J. (2011) Permuting operations on strings and their relation to prime numbers. Discrete Applied Mathematics, 159 (17). pp. 1915-1932. ISSN 0166-218X

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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 $\{X_n\}_{n\geq 2}$ 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 $n$ ($n\geq 2$). 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.
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Copyright:© 2011 Elsevier
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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