Bounding the number of k-faces in arrangements of hyperplanes
We study certain structural problems of arrangements of hyperplanes in d- dimensional Euclidean space. Of special interest are nontrivial relations satisfied by ...
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A lower bound on the number of cells in arrangements of hyperplanes
Lower bounds on the numbers of k-cells in arrangements of hyperplanes are ... < _ k <_ d - 1 the various k-faces of these cells are the k-cells of the arrangement.
[ 1-s2.0-0097316576900273-main.pdf?_tid=d151f024-5aa4-11e5-bc71-00000aacb35f&acdnat=1442210143_a7d34a31d371ba6f31140713710ac8da - Read/Download File
Combinatorial face enumeration in arrangements and oriented
Let fk(F) denote the number of k-dimensional faces of a d-dimensional arrangement ... This algorithm can be applied to any arrangement of hyperplanes in ..... and T. Tokuyama, Bounding the number of k-faces in arrangements of hyperplanes, ...
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Cells with many facets in arrangements of hyperplanes
In Section 3, we consider the average number of hyperplanes bounding the .... Every arrangement of n , 2d + 1 > 5 (pseudo)hyperplanes in pd has at most E,k-(" k' ) ... 1)-dimensional face of Ye belongs to exactly two cells, the average number ...
[ 1-s2.0-0012365X9190375C-main.pdf?_tid=2d2b351e-e740-11e4-b721-00000aab0f26&acdnat=1429522535_4290f5fbdf2d51411e076676dd50594a - Read/Download File
On the Complexity of Many Faces in Arrangements - Duke University
The study of arrangements of lines and hyperplanes has a long, rich history, but ... Many Faces in Arrangements of Pseudo-Segments and Circles upper bound for the maximum value of K(P,Γ), as a function of n and m, for the cases where Γ is ...
[ circular-faces.pdf - Read/Download File
On the Zone of a Surface in a Hyperplane Arrangement
Let H be a collection of n hyperplanes in IRd, let A denote the arrangement of H; and ... We show that the total number of faces bounding the cells of the zone of ... 0 k<d. These cells and faces define a cell complex which is commonly known as.
[ 8727918bd123b53808d83c0db20b269e3175.pdf - Read/Download File
k-Sets and k-Facets - Department of Computer Science - ETH Zürich
for the maximum number of k-facets that an n-point set in general position in Rd .... i.e., that any d of the bounding hyperplanes intersect in exactly one point and that ... the d-dimensional sphere Sd. In such a spherical arrangement, the faces ...
[ kSetSurvey.pdf - Read/Download File
Arrangements of Lines and Hyperplanes - UCSB Computer Science
Nov 16, 2015 ... Similarly, points and hyperplanes in d-space require d parameters, and ... Therefore, under the projective transform, if there are k collinear ... The size of a face is the number of edges bounding it (combinatorial complexity).
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O(nd-1). - Department of Computing and Software
The zone theorem for an arrangement of n hyperplanes in d-dimensional ... the total number of faces bounding the cells intersected by another hyperplane is .... in generic position, i.e., every k hyperplanes in H t2 {b} intersect in a (d k)-flat, for.
[ ess93.pdf - Read/Download File
A Bound on Local Minima of Arrangements that implies the Upper
Let A(H) be a simple arrangement of a set H of n hyperplanes in Ed. For h ∈ H, ... In addition to bounding the number of (≤k)-minima, Mulmuley showed some ..... Theorem 3.2 The number of k-faces of a simple polytope in Ed with n facets.
[ p.pdf - Read/Download File
On the number of Bounding Cycles for Nonlinear Arrangements
In the case of real hyperplane arrangements, the number of bounded regions in the ... faces A on a smooth complete intersection X ⊂ Cn, and consider the .... Φ | XK : XK → K and Φ |X0K : X0K → K are transverse to AK in a punctured ...
[ total.pdf - Read/Download File
Counting facets and incidences - Springer
number of facets bounding m cells in an arrangement of n hyperplanes in R a, for ... K(P, rI) be the number of 2-faces bounding nonempty cells of d(l-l), and let.
[ BF02187848.pdf - Read/Download File
Page 1 SIAM J. COMPUT. © 1986 Society for Industrial and Applied
CONSTRUCTING ARRANGEMENTS OF LINES AND HYPERPLANES ..... now defined as the number of k-faces that bound g, for 0 = k = d –1. The sum of the.
[ 1986-J-07-ArrangementsLinesHyperplanes.pdf - Read/Download File
The cd-index of zonotopes and arrangements - Mathematics
the latter counts the numbers of faces in each dimension, the former counts ... ticular interest in the study of hyperplane arrangements (see [20]), to which they are dual. ... For a field k of characteristic 0, let F be the polynomial algebra in non- ..... bound on the dimension of the span of the flag f-vectors of zonotopes. The.
[ zonotopes.pdf - Read/Download File
Point Location among Hyperplanes and Unidirectional Ray-Shooting
space, for any fixed E >O. Solution B improves this space bound by making E a ... arrangement al(H) of a finite collection H of hyperplanes in Rd is the cell complex induced by the hyperplanes. An element of the complex is called aface, or a k- face if we ... number of pairs of vertices incident upon a common face of d(R) and ...
[ PointLocHyperUniRadyShoot.pdf - Read/Download File
Power Diagrams: Properties, Algorithms and Applications
The close relationship to convex hulls and arrangements of hyperplanes is investigated and exploited. Efficient algorithms that compute the power diagram and its order-k ... space Ed have been studied by a number ofpeople in their original as well ..... and the lower-dimensional faces bounding them), that is, PD( S) is a cell ...
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Projection volumes of hyperplane arrangements - Division of
Shephard then relates the face numbers of a zonotope to its angle sums. ... νk to be the sum of the ν(F) over all k-dimensional faces F of C. The νk are called ... region in the hyperplane arrangement formed by taking the bounding hyperplanes.
[ volumes.pdf - Read/Download File
The Enumeration and Orthant Decomposition of Hyperplane
Moreover, each face and each vertex of a hyperplane arrangement can be ... Note that non-degenerate arrangements maximize the number of vertices and cells. ..... bounding box side (k = 1) and one involves two bounding box sides (k = 0).
[ hyparr.pdf - Read/Download File
A new technique for analyzing substructures in arrangements of
arrangement, and a bound of O(ml/3n 2 + n log 2 n) for the complexity of the vertical ... Let Ck(/2) denote the number of k-level inner vertices in .A(/2), and let ..... Proof. We draw a vertical hyperplane through each (d - 2)-face of every simplex in.
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Notes
Apr 29, 2010 ... closure of all the vertices (intersections of d bounding hyperplanes). ... fp(P) is the number of k-faces of a polytope P. That is f0(P) is the number.
[ polytopes.pdf - Read/Download File
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