### Abstract

Original language | English |
---|---|

Pages (from-to) | 1868-1881 |

Number of pages | 14 |

Journal | Discrete applied mathematics |

Volume | 161 |

Issue number | 13-14 |

DOIs | |

Publication status | Published - Sep 2013 |

### Fingerprint

### Keywords

- HMI-SLT: Speech and Language Technology
- MSC-11A07
- MSC-11N05
- MSC-12E20
- distribution of prime numbers
- Artin's conjecture (on primitive roots)
- Archimedes' spiral
- Twist
- Queneau number
- Shuffle
- Josephus problem
- METIS-297691
- MSC-68R15

### Cite this

*Discrete applied mathematics*,

*161*(13-14), 1868-1881. https://doi.org/10.1016/j.dam.2013.03.002

}

*Discrete applied mathematics*, vol. 161, no. 13-14, pp. 1868-1881. https://doi.org/10.1016/j.dam.2013.03.002

**Permuting Operations on Strings and the Distribution of Their Prime Numbers.** / Asveld, P.R.J.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - Permuting Operations on Strings and the Distribution of Their Prime Numbers

AU - Asveld, P.R.J.

N1 - eemcs-eprint-23421

PY - 2013/9

Y1 - 2013/9

N2 - 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 $n$ {\em $X$-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 on the density of certain sets of prime numbers.

AB - 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 $n$ {\em $X$-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 on the density of certain sets of prime numbers.

KW - HMI-SLT: Speech and Language Technology

KW - MSC-11A07

KW - MSC-11N05

KW - MSC-12E20

KW - distribution of prime numbers

KW - Artin's conjecture (on primitive roots)

KW - Archimedes' spiral

KW - Twist

KW - Queneau number

KW - Shuffle

KW - Josephus problem

KW - METIS-297691

KW - MSC-68R15

U2 - 10.1016/j.dam.2013.03.002

DO - 10.1016/j.dam.2013.03.002

M3 - Article

VL - 161

SP - 1868

EP - 1881

JO - Discrete applied mathematics

JF - Discrete applied mathematics

SN - 0166-218X

IS - 13-14

ER -