Given an n3 configuration, a one-point extension is a technique that constructs (n + 1)3 configurations from it. A configuration is geometric if it can be realized by a collection of points and straight lines in the plane. Given a geometric n3 configuration with a planar coordinatization of its points and lines, a method is presented that uses a one-point extension to produce (n + 1)3 configurations from it, and then constructs geometric realizations of the (n + 1)3 configurations. It is shown that this can be done using only a homogeneous cubic polynomial in just three variables, independent of n. This transforms a computationally intractable problem into a computationally practical one.
@article{1059,
title = {Coordinatizing n3 configurations},
journal = {ARS MATHEMATICA CONTEMPORANEA},
volume = {15},
year = {2018},
doi = {10.26493/1855-3974.1059.4be},
language = {EN},
url = {http://dml.mathdoc.fr/item/1059}
}
Kocay, William L. Coordinatizing n3 configurations. ARS MATHEMATICA CONTEMPORANEA, Tome 15 (2018) . doi : 10.26493/1855-3974.1059.4be. http://gdmltest.u-ga.fr/item/1059/