Results 1 to 10 of about 1,230 (193)
Hyperplane Arrangements in polymake [PDF]
Lecture Notes in Computer Science, 2020 Hyperplane arrangements form the latest addition to the zoo of combinatorial objects dealt with by polymake. We report on their implementation and on a algorithm to compute the associated cell decomposition. The implemented algorithm performs significantly better than brute force alternatives, as it requires less convex hulls computations.
Lars Kästner +2 more
exaly +5 more sources
Multivariate splines and hyperplane arrangements
Journal of Computational and Applied Mathematics, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ren-Hong Wang, Chun-Gang Zhu
exaly +3 more sources
Deformations of Coxeter Hyperplane Arrangements
Journal of Combinatorial Theory - Series A, 2000 33 ...
Alexander Postnikov, Richard P Stanley
exaly +5 more sources
The Monodromy Conjecture for hyperplane arrangements [PDF]
Geometriae Dedicata, 2011 Added: 2.6-2.9 discussing the p-adic ...
Nero Budur +2 more
exaly +6 more sources
Affine and Toric Hyperplane Arrangements [PDF]
Discrete & Computational Geometry, 2009 We extend the Billera-Ehrenborg-Readdy map between the intersection lattice and face lattice of a central hyperplane arrangement to affine and toric hyperplane arrangements. For arrangements on the torus, we also generalize Zaslavsky's fundamental results on the number of regions.
Richard Ehrenborg +2 more
openaire +4 more sources
Combinatorially equivalent hyperplane arrangements [PDF]
Advances in Applied Mathematics, 2021 We study the combinatorics of hyperplane arrangements over arbitrary fields. Specifically, we determine in which situation an arrangement and its reduction modulo a prime number have isomorphic lattices via the use of minimal strong $σ$-Gröbner bases.
Elisa Palezzato, Michele Torielli
openaire +5 more sources
More Bisections by Hyperplane Arrangements [PDF]
Discrete & Computational Geometry, 2021 A union of an arrangement of affine hyperplanes $H$ in $R^d$ is the real algebraic variety associated to the principal ideal generated by the polynomial $p_{H}$ given as the product of the degree one polynomials which define the hyperplanes of the arrangement.
Pavle V. M. Blagojevic +3 more
openaire +2 more sources
Depth in an Arrangement of Hyperplanes [PDF]
Discrete & Computational Geometry, 1999 A collection of \(n\) hyperplanes in \(\mathbb R^d\) forms a hyperplane arrangement. The depth of a point \(\theta\in\mathbb R^d\) is the smallest number of hyperplanes crossed by any ray emanating from \(\theta.\) The authors prove that for \(d = 2\) there always exists a point \(\theta\) with depth at least \(\lceil n/3\rceil.\) This theorem allows ...
Peter J. Rousseeuw, Mia Hubert
openaire +3 more sources
IET Networks, EarlyView., 2022 Abstract Sensor technology advancements have provided a viable solution to fight COVID and to develop healthcare systems based on Internet of Things (IoTs). In this study, image processing and Artificial Intelligence (AI) are used to improve the IoT framework.
Noor M Allayla +2 more
wiley +1 more source
Cell Complexities in Hyperplane Arrangements [PDF]
Discrete and Computational Geometry, 2004 The complexity of some cells of an hyperplane arrangement in \(R^d\) is the total number of faces of all dimensions of these cells. The authors show that the complexity of \(m\) distinct cells in an arrangement of \(n\) hyperplanes in dimension \(d\geq 4\) is \(O(m^{1/2}n^{d/2}\log^{(\lfloor d/2\rfloor-2)}n)\).
Boris Aronov, Micha Sharir
openaire +2 more sources