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Fuzzy Logic for Incidence Geometry [PDF]

open access: yesThe 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   +5 more sources

The pentagon relation and incidence geometry [PDF]

open access: greenJournal 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
openalex   +5 more sources

Convex subspaces of Lie incidence geometries [PDF]

open access: diamondCombinatorial 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
openalex   +3 more sources

Incidence Geometry in a Weyl Chamber I: $GL_n$

open access: greenAdvances 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
openalex   +8 more sources

Ruled surface theory and incidence geometry [PDF]

open access: green, 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
openalex   +3 more sources

Incidence geometry and universality in the tropical plane [PDF]

open access: greenJournal of Combinatorial Theory, Series A, 2017
v2: 20 pages, 20 figures.
Milo Brandt   +3 more
openalex   +4 more sources

An axiom system for incidence spatial geometry

open access: greenRevista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, 2008
Incidence spatial geometry is based on three-sorted structures consisting of points, lines and planes together with three intersort binary relations between points and lines, lines and planes and points and planes. We introduce an equivalent one-sorted geometrical structure, called incidence spatial frame, which is suitable for modal considerations. We
Alfonso Ríder Moyano, Rafael M. Rubio
openalex   +4 more sources

An Incidence Geometry approach to Dictionary Learning [PDF]

open access: yes, 2015
We study the Dictionary Learning (aka Sparse Coding) problem of obtaining a sparse representation of data points, by learning \emph{dictionary vectors} upon which the data points can be written as sparse linear combinations.
Sitharam, Meera   +2 more
core   +2 more sources

Finite projective geometries that are incidence structures of caps

open access: bronzeLinear Algebra and its Applications, 1982
AbstractA t-cap in a geometry is a set of t points no three of which are collinear. A quadric in a projective geometry PG(n, q) is a set of points x which satisfy xTQx = 0,Q being an n + 1 by n + 1 matrix over GF(q). We show that in any Desarguesian projective geometry PG(2n, q), q odd, there exists a family of (q + 1)-caps which obey the axioms for ...
Barbu C. Kestenband
openalex   +3 more sources

The flecnode polynomial: a central object in incidence geometry [PDF]

open access: green, 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 ...
Katz, Nets Hawk
core   +4 more sources

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