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Bounds for the minimum diameter of integral point sets

Title data

Kurz, Sascha ; Laue, Reinhard:
Bounds for the minimum diameter of integral point sets.
Bayreuth , 2019 . - 8 S.

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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

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