@book{5f398dc657934d00b6a8f799d7475211,

title = "Permuting Operations on Strings and Their Relation to Prime Numbers",

abstract = "Some length-preserving operations on strings only permute the symbol positions in strings; such an operation $X$ gives rise to a family $\{X_n\}_{n\geq2}$ of similar permutations. We investigate the structure and the order of the cyclic group generated by $X_n$. We call an integer $n$ $X$-{\em 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. 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.",

keywords = "Operation on strings, MSC-11A41, Josephus problem, Queneau number, Twist, IR-71704, METIS-270843, Shuffle, MSC-11A07, HMI-SLT: Speech and Language Technology, MSC-68R15, prime number, EWI-17983",

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

note = "eemcs-eprint-17983 ",

year = "2010",

month = jun,

day = "7",

language = "Undefined",

series = "CTIT Technical Report Series",

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

number = "TR-CTIT-10-22",

address = "Netherlands",

}