combinatorial geometries

Noun

combinatorial geometry (countable and uncountable, plural combinatorial geometries)

1. (uncountable) The field of mathematics which examines extremal problems of a combinatorial nature expressed geometrically.
   • The generation of combinatorial types of point configurations and hyperplane arrangements point configurations and hyperplane arrangements has long been an outstanding problem of combinatorial geometry.2003, Lukas Finschi, Komei Fukuda, “Combinatorial Generation of Small Point Configurations and Hyperplane Arrangements”, in Boris Aronov, Saugata Basu, Janos Pach, Micha Sharir, editors, Discrete and...
2. (countable, theory of matroids) A simple matroid.
   • For the generation of these combinatorial types no direct method is known, and it appears to be necessary to use combinatorial abstractions — allowable sequences of permutations, #92;lambda-functions, chirotopes, combinatorial geometries, or oriented matroids; in our work we will use oriented...2003, Lukas Finschi, Komei Fukuda, “Combinatorial Generation of Small Point Configurations and Hyperplane Arrangements”, in Boris Aronov, Saugata Basu, Janos Pach, Micha Sharir, editors, Discrete and...