@book{ac31cb4d12cb451089b787acefcc8698,

title = "Permuting Operations on Strings: Their Permutations and Their Primes",

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 the Archimedes spiral. Such a permuting operation $X$ gives rise to a family $\{X_n\}_{n\geq2}$ of similar permutations. We investigate the structure and the order of the cyclic group generated by such a permutation $X_n$. We call an integer $n$ $X$-prime if $X_n$ 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.",

keywords = "Josephus problem, Shuffle, permutation, Operation on strings, cyclic subgroup, EWI-15655, distribution of prime numbers, prime number, MSC-68R15, HMI-SLT: Speech and Language Technology, MSC-11A07, Twist, IR-67513, MSC-11A41, METIS-263904",

author = "P.R.J. Asveld",

note = "eemcs-eprint-15655 ",

year = "2009",

month = jun,

day = "30",

language = "Undefined",

series = "CTIT Technical Report Series",

publisher = "Centre for Telematics and Information Technology (CTIT)",

number = "TR-CTIT-09-26",

address = "Netherlands",

}