Results 1 to 10 of about 3,366,340 (357)
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
doaj +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
Incidence geometry and universality in the tropical plane [PDF]
Journal of Combinatorial Theory, Series A Volume 159, October
2018, Pages 26-53, 2017 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. This study leads naturally to a discussion of the realizability of incidence data of tropical lines.
Milo Brandt +3 more
arxiv +5 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
An incidence Hopf Algebra of Convex Geometries [PDF]
arXiv, 2012 A lattice L is "meet-distributive" if for each element of L, the meets of the elements directly below it form a Boolean lattice. These objects are in bijection with "convex geometries", which are an abstract model of convexity. Do they give rise to an incidence Hopf algebra of convex geometries?
Fabian Latorre
arxiv +5 more sources
The flecnode polynomial: a central object in incidence geometry [PDF]
arXiv, 2014 We give a brief exposition of the proof of the Cayley-Salmon theorem and its recent role in incidence geometry. Even when we don't use the properties of ruled surfaces explicitly, the regime in which we have interesting results in point-line incidence problems often coincides with the regime in which lines are organized into ruled surfaces.
Katz, Nets Hawk
arxiv +7 more sources
FinInG: a package for Finite Incidence Geometry [PDF]
arXiv, 2016 FinInG is a package for computation in Finite Incidence Geometry. It provides users with the basic tools to work in various areas of finite geometry from the realms of projective spaces to the flat lands of generalised polygons. The algebraic power of GAP is exploited, particularly in its facility with matrix and permutation groups.
John Bamberg +5 more
arxiv +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