Results 1 to 10 of about 3,180,129 (338)
Fuzzy Logic for Incidence Geometry [PDF]
The Scientific World Journal, 2016 The paper presents a mathematical framework for approximate geometric reasoning with extended objects in the context of Geography, in which all entities and their relationships are described by human language. These entities could be labelled by commonly
Alex Tserkovny
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Incidence geometry and universality in the tropical plane [PDF]
Journal of Combinatorial Theory, Series A, 2018 We examine the incidence geometry of lines in the tropical plane. We prove tropical analogs of the Sylvester-Gallai and Motzkin-Rabin theorems in classical incidence geometry.
Brandt, Milo +3 more
core +6 more sources
Incidence Geometry in a Weyl Chamber I: $GL_n$ [PDF]
Advances in Applied Mathematics, 2015 We study the central hyperplane arrangement whose hyperplanes are the vanishing loci of the weights of the first and the second fundamental representations of $\mathfrak{gl}_n$ restricted to the dual fundamental Weyl chamber. We obtain generating functions that count flats and faces of a given dimension.
Mboyo Esole +3 more
semanticscholar +10 more sources
The pentagon relation and incidence geometry [PDF]
Journal of Mathematical Physics, 2014 We define a map \documentclass[12pt]{minimal}\begin{document}$S:{\mathbb {D}}^2\times {\mathbb {D}}^2 \dashrightarrow {\mathbb {D}}^2\times {\mathbb {D}}^2$\end{document}S:D2×D2⤏D2×D2, where \documentclass[12pt]{minimal}\begin{document}${\mathbb {D}}$\end{document}D is an arbitrary division ring (skew field), associated with the Veblen configuration ...
Adam Doliwa, С. М. Сергеев
semanticscholar +7 more sources
Bulletin of the American Mathematical Society, 1940 The purpose of this note is to analyze the conditions needed in geometry to introduce ideal points without using order relations. Since only incidence relations are used, it is convenient to use the notation of lattice theory.
Saul Gorn
semanticscholar +4 more sources
Ruled surface theory and incidence geometry [PDF]
, 2016 This is an expository paper about applications of ruled surface theory in incidence geometry. It surveys the results that have been proven, gives an overview of the methods, and discusses some open problems and further directions. It will appear in the book Journey Through Discrete Mathematics, a Tribute to Jiri Matousek, edited by Martin Loebl ...
Larry Guth
semanticscholar +5 more sources
Sum-product theorems and incidence geometry
Journal of the European Mathematical Society, 2007 In this paper we prove the following theorems in incidence geometry. The main ingredients used are the subspace theorem, Balog–Szemerédi–Gowers Theorem, and Szemerédi–Trotter Theorem. We also generalize the theorems to high dimensions, extend Theorem 1 to \Bbb F_p^2 , and ...
Mei-Chu Chang, József Solymosi
semanticscholar +5 more sources
Point-hyperplane Incidence Geometry and the Log-rank Conjecture [PDF]
ACM Transactions on Computation Theory, 2022 We study the log-rank conjecture from the perspective of point-hyperplane incidence geometry. We formulate the following conjecture: Given a point set in ℝd that is covered by constant-sized sets of parallel hyperplanes, there exists an affine subspace ...
Noah Singer, Madhu Sudan
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Convex subspaces of Lie incidence geometries [PDF]
Combinatorial Theory, 2022 We classify the convex subspaces of all hexagonic Lie incidence geometries (among which all long root geometries of spherical Tits-buildings). We perform a similar classification for most other Lie incidence geometries of spherical Tits-buildings, in particular for all projective and polar Grassmannians, and for exceptional Grassmannians of diameter at
Jeroen Meulewaeter +1 more
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Crystals, 2019 The in-plane magnetic structure of a layered system composed of polycrystalline grains smaller than the ferromagnetic exchange length was studied to elucidate the mechanism controlling the magnetic properties considerably different from the bulk using ...
Ryuji Maruyama +5 more
doaj +2 more sources