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 mdimensional 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 233240, 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.unibayreuth.de/id/eprint/4529 