Coordinatizing n3 configurations

William L. Kocay

Abstract


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.

Keywords


(n,3)-configuration, geometric configuration, anti-Pappian, rational coordinatization, elliptic curve

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DOI: https://doi.org/10.26493/1855-3974.1059.4be

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications