Desargues theorem, its configurations, and the solution to a long-standing enumeration problem

2020/07/17 by Aiden A. Bruen, Bruen, Aiden A., Trevor C. Bruen +3
Mathematics · #51A30 #51E15 #Advanced Mathematical Theories #Combinatorics (math.CO) #FOS: Mathematics #History and Theory of Mathematics #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2007.09175

openalex publication_date 2020/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We solve a long-standing problem by enumerating the number of non-degenerate Desargues configurations. We extend the result to the more difficult case involving Desargues blockline structures in Section 8. A transparent proof of Desargues theorem in the plane and in space is presented as a by-product of our methods.

Citations

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