@book{66023eaaf2a24fdd976ff5a19fae6072,

title = "Permuting Operations on Strings and the Distribution of Their Prime Numbers",

abstract = "Several ways of interleaving, as studied in theoretical computer science, and some subjects from mathematics can be modeled by length-preserving operations on strings, that only permute the symbol positions in strings. Each such operation $X$ gives rise to a family $\{X_n\}_{n\geq2}$ of similar permutations. We call an integer $n$ $X$-{\em prime} if $X_n$ consists of a single cycle of length $n$ ($n\geq2$). For some instances of $X$ ---such as shuffle, twist, operations based on the Archimedes' spiral and on the Josephus problem--- we investigate the distribution of $X$-primes and of the associated (ordinary) prime numbers, which leads to variations of some well-known conjectures in number theory.",

keywords = "MSC-68R15, EWI-20685, distribution of prime numbers, Shuffle, Josephus problem, Queneau number, Twist, Artin's conjecture (on primitive roots), Archimedes' spiral, IR-78281, METIS-278873, MSC-11B25, MSC-11A41, MSC-11A07, HMI-SLT: Speech and Language Technology",

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

note = "eemcs-eprint-20685 ",

year = "2011",

month = oct,

day = "17",

language = "Undefined",

series = "CTIT Technical Report Series",

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

number = "TR-CTIT-11-24",

address = "Netherlands",

}