One-point extensions in n_3 configurations
| Autor: | William L. Kocay |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Algebra and Number Theory
Plane (geometry) Desargues configuration 020206 networking & telecommunications 0102 computer and information sciences 02 engineering and technology Fano plane Extension (predicate logic) 01 natural sciences Theoretical Computer Science Combinatorics 010201 computation theory & mathematics 0202 electrical engineering electronic engineering information engineering Discrete Mathematics and Combinatorics Point (geometry) Geometry and Topology Mathematics |
| Zdroj: | Ars Mathematica Contemporanea. 10:291-322 |
| ISSN: | 1855-3974 1855-3966 |
| DOI: | 10.26493/1855-3974.758.bec |
| Popis: | Given an n 3 configuration, a 1-point extension is a technique that constructs an ( n + 1) 3 configuration from it. It is proved that all ( n + 1) 3 configurations can be constructed from an n 3 configuration using a 1-point extension, except for the Fano, Pappus, and Desargues configurations, and a family of Fano-type configurations. A 3-point extension is also described. A 3-point extension of the Fano configuration produces the Desargues and anti-Pappian configurations. The significance of the 1-point extension is that it can frequently be used to construct real and/or rational coordinatizations in the plane of an ( n + 1) 3 configuration, whenever it is geometric, and the corresponding n 3 configuration is also geometric. |
| Databáze: | OpenAIRE |
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