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...

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...

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

if and only if the vector b lies in the image of the linear transformation A. Arrangement of hyperplanes Iterative refinement Coates graph LAPACK (the...

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...

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

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

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...

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

. 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...

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...

Edelsbrunner, H.; O'Rourke, J.; Seidel, R. (1986), "Constructing arrangements of lines and hyperplanes with applications", SIAM Journal on Computing, 15 (2): 341–363...

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

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...

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

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...

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...

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

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...

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...

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

{\displaystyle d} , considering arrangements of hyperplanes, the complexity of the zone of a hyperplane h {\displaystyle h} is the number of facets ( d − 1 {\displaystyle...

complements to hypersurfaces in projective spaces and the topology of arrangements of hyperplanes. In the early 90s he started work on interactions between algebraic...

shortness exponent of polytopes. Chapter 18 studies arrangements of hyperplanes and their dual relation to the combinatorial structure of zonotopes. A concluding...

of the coordinate hyperplanes in the coordinate system given above (i.e. the planes determined by xi = 0). The cross-section of {3,4,3,3} by one of these...

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...