## Title data

Kurz, Sascha ; Laue, Reinhard:

**Bounds for the minimum diameter of integral point sets.**

Bayreuth
,
2019
. - 8 S.

PDF
upper_bounds_for_integral_point_sets.pdf - Published Version Available under License Creative Commons BY 4.0: Attribution . Download (349kB) |

## Abstract

Geometrical objects with integral sides have attracted mathematicians for ages. For example, the problem to prove or to disprove the existence of a perfect box, that is, a rectangular parallelepiped with all edges, face diagonals and space diagonals of integer lengths, remains open. More generally an integral point set P is a set of n points in the m-dimensional Euclidean space with pairwise integral distances where the largest occurring distance is called its diameter. From the combinatorial point of view there is a natural interest in the determination of the smallest possible diameter d(m,n) for given parameters m and n. We give some new upper bounds for the minimum diameter d(m,n) and some exact values.

## Further data

Item Type: | Preprint, postprint |
---|---|

Additional notes (visible to public): | In: The Australasian Journal of Combinatorics, Vol. 39, Pages 233-240, 2007 |

Keywords: | integral distances; diameter |

Subject classification: | Mathematics Subject Classification Code: 52C10 (11D99) |

DDC Subjects: | 000 Computer Science, information, general works > 004 Computer science 500 Science > 510 Mathematics |

Institutions of the University: | Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Former Professors Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematical Economics Faculties |

Language: | English |

Originates at UBT: | Yes |

Date Deposited: | 12 Nov 2019 07:32 |

Last Modified: | 12 Nov 2019 07:32 |

URI: | https://epub.uni-bayreuth.de/id/eprint/4529 |