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...

case the hyperplanes are the (n − 1)-dimensional "flats", each of which separates the space into two half spaces. A reflection across a hyperplane is a kind...

refer to: Arrangement (space partition), a partition of the space by a set of objects of a certain type Arrangement of hyperplanes Arrangement of lines Vertex...

one of counting the cells in an arrangement of lines; for generalizations to higher dimensions, see arrangement of hyperplanes. The analogue of this...

arrangement may have. After Steiner, the study of arrangements turned to higher-dimensional arrangements of hyperplanes, focusing on their overall structure and...

such as hyperplanes or spheres. For a set A {\displaystyle A} of objects in R d {\displaystyle \mathbb {R} ^{d}} , the cells in the arrangement are the...

supersolvable arrangement is a hyperplane arrangement that has a maximal flag consisting of modular elements. Equivalently, the intersection semilattice of the...

image of the linear transformation A. Arrangement of hyperplanes Iterative refinement – Method to improve accuracy of numerical solutions to systems of linear...

form a monoid under composition. The product of faces of an arrangement of hyperplanes. A left identity of a semigroup S (or more generally, magma) is...

. A real hyperplane arrangement A = { H 1 , … , H n } {\displaystyle {\mathcal {A}}=\{H_{1},\ldots ,H_{n}\}} is a finite set of hyperplanes in R d {\displaystyle...

Orlik and Louis Solomon, a pioneer of the theory of arrangements of hyperplanes. He was awarded a Mathematical Society of Japan Algebra Prize in 2010. Terao...

to the combinatorics of arranging a number of hyperplanes in complex N-space (see arrangement of hyperplanes). Special hypergeometric functions occur as...

higher dimensions, i.e. for certain arrangements of hyperplanes, the alternating sum of volumes cut out by the hyperplanes is zero. Compare with the ham sandwich...

complement of the complexification of the arrangement of its reflecting hyperplanes; the generalized braid group of W is the fundamental group of the quotient...

One important example is the case of arrangements of hyperplanes. An arrangement of n hyperplanes defines O(nd) cells, but point location can be performed...

the number of comparisons. The proof of this bound relates X + Y {\displaystyle X+Y} sorting to the complexity of an arrangement of hyperplanes in high-dimensional...

lattice of flats of a graphic matroid can also be realized as the lattice of a hyperplane arrangement, in fact as a subset of the braid arrangement, whose...

Fukuda in 1991, for problems of generating the vertices of convex polytopes and the cells of arrangements of hyperplanes. They were formalized more broadly...

of an arrangement of hyperplanes with a supersolvable intersection lattice is a Koszul algebra. For more information, see Supersolvable arrangement....

University, 29: 165–170 Orlik, Peter; Terao, Hiroaki (1992), Arrangements of Hyperplanes, Grundlehren der mathematischen Wissenschaften, vol. 300, Springer-Verlag...

interpretation of Whitney numbers through arrangements of hyperplanes, zonotopes, non-Radon partitions, and orientations of graphs". Transactions of the American...

Hiroaki Terao, a pioneer of the theory of arrangements of hyperplanes in complex space. In 2012 he was elected a Fellow of the American Mathematical...

set of ν ( d ) {\displaystyle \nu (d)} hyperplanes in general position in d-dimensional real projective space form an arrangement of hyperplanes in which...

theory, and arrangements of hyperplanes. She is a professor emeritus of mathematics at Arizona State University, and deputy director of the Mathematical...

subgroup of the affine group of E that is generated by a set of affine reflections of E (without the requirement that the reflection hyperplanes pass through...

S2CID 122181810. Schechtman, Vadim V.; Varchenko, Alexander N. (1991). "Arrangement of hyperplanes and Lie algebra homology". Inventiones Mathematicae. 106: 139–194...

arrangements of hyperplanes in higher-dimensional spaces. Beyond line arrangements, the same bound as Roberts's theorem holds for arrangements of pseudolines...

combinatorics Alternating sign matrix Almost disjoint sets Antichain Arrangement of hyperplanes Assignment problem Quadratic assignment problem Audioactive decay...

triangulation for two- and three-dimensional data, arrangements of hyperplanes, of line segments, and of triangles, Voronoi diagrams, and Delaunay triangulations...

problem; their algorithm generates all of the vertices of a convex polytope or, dually, of an arrangement of hyperplanes.[AF92][AF96] Birth year from VIAF...