Constructing 7-Clusters

Kurz, Sascha, et al. "Constructing 7-Clusters." Serdica Journal of Computing 8.1 (2014): 47-70. <http://eudml.org/doc/268675>.

@article{Kurz2014,
abstract = {ACM Computing Classification System (1998): G.2, G.4.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 integers 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. Along the way, we have exhaustively determined all Heronian triangles with largest edge length up to 6 · 10^6.},
author = {Kurz, Sascha, Noll, Landon Curt, Rathbun, Randall, Simmons, Chuck},
journal = {Serdica Journal of Computing},
keywords = {Erdos Problems; Integral Point Sets; Heron Triangles; Exhaustive Enumeration},
language = {eng},
number = {1},
pages = {47-70},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Constructing 7-Clusters},
url = {http://eudml.org/doc/268675},
volume = {8},
year = {2014},
}

TY - JOUR
AU - Kurz, Sascha
AU - Noll, Landon Curt
AU - Rathbun, Randall
AU - Simmons, Chuck
TI - Constructing 7-Clusters
JO - Serdica Journal of Computing
PY - 2014
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 8
IS - 1
SP - 47
EP - 70
AB - ACM Computing Classification System (1998): G.2, G.4.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 integers 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. Along the way, we have exhaustively determined all Heronian triangles with largest edge length up to 6 · 10^6.
LA - eng
KW - Erdos Problems; Integral Point Sets; Heron Triangles; Exhaustive Enumeration
UR - http://eudml.org/doc/268675
ER -