About: Arrangement of hyperplanes

Facets (new session)
Description
Metadata
Settings
- Rule:
- Inverse Functional Properties:
- "Same As":

About: Arrangement of hyperplanes Goto Sponge NotDistinct Permalink

An Entity of Type : dbo:MusicalWork, within Data Space : dbpedia.org associated with source document(s)
QRcode icon

http://dbpedia.org/describe/?url=http%3A%2F%2Fdbpedia.org%2Fresource%2FArrangement_of_hyperplanes

In geometry and combinatorics, an arrangement of hyperplanes is an arrangement of a finite set A of hyperplanes in a linear, affine, or projective space S. Questions about a hyperplane arrangement A generally concern geometrical, topological, or other properties of the complement, M(A), which is the set that remains when the hyperplanes are removed from the whole space. One may ask how these properties are related to the arrangement and its intersection semilattice.The intersection semilattice of A, written L(A), is the set of all subspaces that are obtained by intersecting some of the hyperplanes; among these subspaces are S itself, all the individual hyperplanes, all intersections of pairs of hyperplanes, etc. (excluding, in the affine case, the empty set). These intersection subspaces o

Attributes	Values
rdf:type	musical work
rdfs:label	Arrangement of hyperplanes (en)
rdfs:comment	In geometry and combinatorics, an arrangement of hyperplanes is an arrangement of a finite set A of hyperplanes in a linear, affine, or projective space S. Questions about a hyperplane arrangement A generally concern geometrical, topological, or other properties of the complement, M(A), which is the set that remains when the hyperplanes are removed from the whole space. One may ask how these properties are related to the arrangement and its intersection semilattice.The intersection semilattice of A, written L(A), is the set of all subspaces that are obtained by intersecting some of the hyperplanes; among these subspaces are S itself, all the individual hyperplanes, all intersections of pairs of hyperplanes, etc. (excluding, in the affine case, the empty set). These intersection subspaces o (en)
foaf:depiction
dcterms:subject	Discrete geometry Oriented matroids Combinatorics
Wikipage page ID	864438 (xsd:integer)
Wikipage revision ID	1115076379 (xsd:integer)
Link from a Wikipage to another Wikipage	Projective geometry Supersolvable arrangement Euclidean subspace De Rham cohomology Incidence algebra Polyhedron Ranked poset Complex number Geometric lattice Geometry Convex polygon Arrangement (space partition) Discrete geometry Oriented matroids Line (mathematics) Simplex Combinatorics Ideal (ring theory) Polygon Matroid McMullen problem Oriented matroid Affine space Alexander Varchenko American Mathematical Society Combinatorics Exterior algebra Isomorphic Tetrahedron Hyperplane Arrangement of lines Affine geometry Codimension Cohomology Triangle Differential form Plane (mathematics) Poset Real number Real projective space Chain complex Semilattice Root system Smith normal form Parallelogram Polytope Weyl group Transactions of the American Mathematical Society Linear space dbr:Geometric_semilattice dbr:Orlik–Solomon_algebra dbr:Semimatroid
sameAs	Arrangement of hyperplanes Arrangement of hyperplanes Arrangement of hyperplanes Arrangement of hyperplanes
dbp:wikiPageUsesTemplate	dbt:Springer dbt:Citation dbt:Cite_book dbt:Harv dbt:Harvtxt dbt:Short_description
thumbnail	wiki-commons:Special:FilePath/Arrangement_hyperplans.png?width=300
id	A/a110700 (en)
title	Arrangement of hyperplanes (en)
has abstract	In geometry and combinatorics, an arrangement of hyperplanes is an arrangement of a finite set A of hyperplanes in a linear, affine, or projective space S. Questions about a hyperplane arrangement A generally concern geometrical, topological, or other properties of the complement, M(A), which is the set that remains when the hyperplanes are removed from the whole space. One may ask how these properties are related to the arrangement and its intersection semilattice.The intersection semilattice of A, written L(A), is the set of all subspaces that are obtained by intersecting some of the hyperplanes; among these subspaces are S itself, all the individual hyperplanes, all intersections of pairs of hyperplanes, etc. (excluding, in the affine case, the empty set). These intersection subspaces of A are also called the flats of A. The intersection semilattice L(A) is partially ordered by reverse inclusion. If the whole space S is 2-dimensional, the hyperplanes are lines; such an arrangement is often called an arrangement of lines. Historically, real arrangements of lines were the first arrangements investigated. If S is 3-dimensional one has an arrangement of planes. (en)
gold:hypernym	Arrangement
prov:wasDerivedFrom	wikipedia-en:Arrangement_of_hyperplanes?oldid=1115076379&ns=0
page length (characters) of wiki page	12927 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Arrangement_of_hyperplanes
is Link from a Wikipage to another Wikipage of	Supersolvable arrangement Algorithmic Geometry Arrangement (disambiguation) Curtis Greene Index of combinatorics articles Zone theorem Chromatic polynomial Generalized hypergeometric function Convex Polytopes Matroid McMullen problem CGAL Mirrors and Reflections Oriented matroid Semigroup Discrete geometry Graphic matroid Knizhnik–Zamolodchikov equations Hiroaki Terao Hyperplane

Faceted Search & Find service v1.17_git139 as of Feb 29 2024

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 08.03.3330 as of Mar 19 2024, on Linux (x86_64-generic-linux-glibc212), Single-Server Edition (61 GB total memory, 49 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software