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- Arrangement_of_hyperplanes 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 subspaces are called the flats of A. 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.".
- Arrangement_of_hyperplanes thumbnail Arrangement_hyperplans.png?width=300.
- Arrangement_of_hyperplanes wikiPageID "864438".
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- Arrangement_of_hyperplanes wikiPageRevisionID "639677891".
- Arrangement_of_hyperplanes wikiPageWikiLink Affine_geometry.
- Arrangement_of_hyperplanes wikiPageWikiLink Affine_space.
- Arrangement_of_hyperplanes wikiPageWikiLink American_Mathematical_Society.
- Arrangement_of_hyperplanes wikiPageWikiLink Arrangement_(space_partition).
- Arrangement_of_hyperplanes wikiPageWikiLink Arrangement_of_lines.
- Arrangement_of_hyperplanes wikiPageWikiLink Category:Combinatorics.
- Arrangement_of_hyperplanes wikiPageWikiLink Category:Discrete_geometry.
- Arrangement_of_hyperplanes wikiPageWikiLink Category:Oriented_matroids.
- Arrangement_of_hyperplanes wikiPageWikiLink Chain_complex.
- Arrangement_of_hyperplanes wikiPageWikiLink Codimension.
- Arrangement_of_hyperplanes wikiPageWikiLink Cohomology.
- Arrangement_of_hyperplanes wikiPageWikiLink Combinatorics.
- Arrangement_of_hyperplanes wikiPageWikiLink Complex_number.
- Arrangement_of_hyperplanes wikiPageWikiLink Convex_polygon.
- Arrangement_of_hyperplanes wikiPageWikiLink De_Rham_cohomology.
- Arrangement_of_hyperplanes wikiPageWikiLink Differential_form.
- Arrangement_of_hyperplanes wikiPageWikiLink Euclidean_subspace.
- Arrangement_of_hyperplanes wikiPageWikiLink Flat_(geometry).
- Arrangement_of_hyperplanes wikiPageWikiLink Geometric_lattice.
- Arrangement_of_hyperplanes wikiPageWikiLink Geometric_semilattice.
- Arrangement_of_hyperplanes wikiPageWikiLink Geometry.
- Arrangement_of_hyperplanes wikiPageWikiLink Hyperplane.
- Arrangement_of_hyperplanes wikiPageWikiLink Ideal_(ring_theory).
- Arrangement_of_hyperplanes wikiPageWikiLink Incidence_algebra.
- Arrangement_of_hyperplanes wikiPageWikiLink Isomorphic.
- Arrangement_of_hyperplanes wikiPageWikiLink Isomorphism.
- Arrangement_of_hyperplanes wikiPageWikiLink Line_(geometry).
- Arrangement_of_hyperplanes wikiPageWikiLink Line_(mathematics).
- Arrangement_of_hyperplanes wikiPageWikiLink Linear_space.
- Arrangement_of_hyperplanes wikiPageWikiLink Matroid.
- Arrangement_of_hyperplanes wikiPageWikiLink McMullen_problem.
- Arrangement_of_hyperplanes wikiPageWikiLink Orlik–Solomon_algebra.
- Arrangement_of_hyperplanes wikiPageWikiLink Parallelogram.
- Arrangement_of_hyperplanes wikiPageWikiLink Partially_ordered_set.
- Arrangement_of_hyperplanes wikiPageWikiLink Plane_(geometry).
- Arrangement_of_hyperplanes wikiPageWikiLink Plane_(mathematics).
- Arrangement_of_hyperplanes wikiPageWikiLink Polygon.
- Arrangement_of_hyperplanes wikiPageWikiLink Polyhedron.
- Arrangement_of_hyperplanes wikiPageWikiLink Polytope.
- Arrangement_of_hyperplanes wikiPageWikiLink Poset.
- Arrangement_of_hyperplanes wikiPageWikiLink Projective_geometry.
- Arrangement_of_hyperplanes wikiPageWikiLink Ranked_poset.
- Arrangement_of_hyperplanes wikiPageWikiLink Real_number.
- Arrangement_of_hyperplanes wikiPageWikiLink Real_projective_space.
- Arrangement_of_hyperplanes wikiPageWikiLink Root_system.
- Arrangement_of_hyperplanes wikiPageWikiLink Semilattice.
- Arrangement_of_hyperplanes wikiPageWikiLink Semimatroid.
- Arrangement_of_hyperplanes wikiPageWikiLink Simplex.
- Arrangement_of_hyperplanes wikiPageWikiLink Supersolvable_arrangement.
- Arrangement_of_hyperplanes wikiPageWikiLink Tetrahedron.
- Arrangement_of_hyperplanes wikiPageWikiLink Transactions_of_the_American_Mathematical_Society.
- Arrangement_of_hyperplanes wikiPageWikiLink Triangle.
- Arrangement_of_hyperplanes wikiPageWikiLink Vector_space.
- Arrangement_of_hyperplanes wikiPageWikiLink Weyl_group.
- Arrangement_of_hyperplanes wikiPageWikiLink File:Arrangement_hyperplans.png.
- Arrangement_of_hyperplanes wikiPageWikiLinkText "Arrangement of hyperplanes".
- Arrangement_of_hyperplanes wikiPageWikiLinkText "Arrangement of hyperplanes#Polynomials".
- Arrangement_of_hyperplanes wikiPageWikiLinkText "Arrangement".
- Arrangement_of_hyperplanes wikiPageWikiLinkText "Hyperplane arrangements".
- Arrangement_of_hyperplanes wikiPageWikiLinkText "arrangement of hyperplanes".
- Arrangement_of_hyperplanes wikiPageWikiLinkText "arrangement".
- Arrangement_of_hyperplanes wikiPageWikiLinkText "arrangements of hyperplanes".
- Arrangement_of_hyperplanes wikiPageWikiLinkText "hyperplane arrangement".
- Arrangement_of_hyperplanes wikiPageWikiLinkText "hyperplane complements".
- Arrangement_of_hyperplanes hasPhotoCollection Arrangement_of_hyperplanes.
- Arrangement_of_hyperplanes id "A/a110700".
- Arrangement_of_hyperplanes title "Arrangement of hyperplanes".
- Arrangement_of_hyperplanes wikiPageUsesTemplate Template:Citation.
- Arrangement_of_hyperplanes wikiPageUsesTemplate Template:Cite_book.
- Arrangement_of_hyperplanes wikiPageUsesTemplate Template:Harv.
- Arrangement_of_hyperplanes wikiPageUsesTemplate Template:Harvtxt.
- Arrangement_of_hyperplanes wikiPageUsesTemplate Template:Springer.
- Arrangement_of_hyperplanes subject Category:Combinatorics.
- Arrangement_of_hyperplanes subject Category:Discrete_geometry.
- Arrangement_of_hyperplanes subject Category:Oriented_matroids.
- Arrangement_of_hyperplanes hypernym Arrangement.
- Arrangement_of_hyperplanes type MusicalWork.
- Arrangement_of_hyperplanes type Combinatoric.
- Arrangement_of_hyperplanes type Field.
- Arrangement_of_hyperplanes 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.".
- Arrangement_of_hyperplanes label "Arrangement of hyperplanes".
- Arrangement_of_hyperplanes sameAs Category:Hyperplane_arrangements.
- Arrangement_of_hyperplanes sameAs m.03jlnb.
- Arrangement_of_hyperplanes sameAs Hyperplane_arrangements.
- Arrangement_of_hyperplanes sameAs Q4795851.
- Arrangement_of_hyperplanes sameAs Q4795851.
- Arrangement_of_hyperplanes wasDerivedFrom Arrangement_of_hyperplanes?oldid=639677891.
- Arrangement_of_hyperplanes depiction Arrangement_hyperplans.png.
- Arrangement_of_hyperplanes isPrimaryTopicOf Arrangement_of_hyperplanes.