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Constructing 7-clusters

URN to cite this document: urn:nbn:de:bvb:703-epub-1786-0

Title data

Kurz, Sascha ; Noll, Landon Curt ; Rathbun, Randall ; Simmons, Chuck:
Constructing 7-clusters.
Bayreuth , 2014 . - 15 S.

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Abstract

A set of n lattice points in the plane, no three on a line and no four on a circle, such that all pairwise distances and coordinates are integral is called an n-cluster (in R^2). We determine the smallest 7-cluster with respect to its diameter. Additionally we provide a toolbox of algorithms which allowed us to computationally locate over 1000 different 7-clusters, some of them having huge integer edge lengths. On the way, we have exhaustively determined all Heronian triangles with largest edge length up to 6 millions.

Further data

Item Type: Preprint, postprint
Additional notes (visible to public): erscheint in: Serdica Journal of Computing
Keywords: Erdös problems; integral point sets; Heron triangles; exhaustive enumeration
DDC Subjects: 500 Science > 510 Mathematics
Institutions of the University: Faculties
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 > Chair Mathematics in Economy
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics in Economy > Chair Mathematics in Economy - Univ.-Prof. Dr. Jörg Rambau
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-1786-0
Date Deposited: 24 Nov 2014 09:57
Last Modified: 14 Mar 2019 15:41
URI: https://epub.uni-bayreuth.de/id/eprint/1786

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