2010/02/01 by David G. Glynn · 8 citations
Computer Science · Engineering · Mathematics · #Combinatorics #Complex projective space #Differential geometry #Digital Image Processing Techniques #Discrete mathematics #Geometry #Graph #Mathematics #Mathematics and Applications #Plane (geometry) #Point (geometry) #Projective geometry #Projective plane #Projective space #Projective test #Pure mathematics #Real projective plane #graph theory and CDMA systems
paper · pdf · doi:10.1017/s1446788708080981
published in Journal of the Australian Mathematical Society 88(1), 75-92 (Cambridge University Press)
openalex publication_date 2010/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
Abstract We discuss n 4 configurations of n points and n planes in three-dimensional projective space. These have four points on each plane, and four planes through each point. When the last of the 4 n incidences between points and planes happens as a consequence of the preceding 4 n −1 the configuration is called a ‘theorem’. Using a graph-theoretic search algorithm we find that there are two 8 4 and one 9 4 ‘theorems’. One of these 8 4 ‘theorems’ was already found by Möbius in 1828, while the 9 4 ‘theorem’ is related to Desargues’ ten-point configuration. We prove these ‘theorems’ by various methods, and connect them with other questions, such as forbidden minors in graph theory, and sets of electrons that are energy minimal.