Permuting operations on strings: Their permutations and their primes


Asveld, Peter R.J. (2009) Permuting operations on strings: Their permutations and their primes. [Report]

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Abstract:We study some length-preserving operations on strings that permute the symbol positions in strings. These operations include some well-known examples (reversal, circular or cyclic shift, shuffle, twist, operations induced by the Josephus problem) and some new ones based on Archimedes spiral. Such a permuting operation $X$ gives rise to a family $\{p(X,n)\}_{n\geq2}$ of similar permutations. We investigate the structure and the order of the cyclic group generated by such a permutation $p(X,n)$. We call an integer $n$ $X$-prime if $p(X,n)$ consists of a single cycle of length $n$ ($n\geq2$). 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.
Item Type:Report
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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