Results 11 to 20 of about 312,013 (185)
Hyperplane Arrangements in the Grassmannian [PDF]
Le MatematicheThe Euler characteristic of a very affine variety encodes the algebraic complexity of solving likelihood (or scattering) equations on this variety. We study this quantity for the Grassmannian with $d$ hyperplane sections removed. We provide a combinatorial formula, and explain how to compute this Euler characteristic in practice, both symbolically and ...
E. Mazzucchelli, D. Pavlov, K. Wang
core +7 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 +6 more sources
Lattice Sums of Hyperplane Arrangements [PDF]
, 2023 39 pages, 4 ...
Yasushi, Komori +2 more
openaire +3 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
Hyperplane arrangements with a lattice of regions [PDF]
Discrete & Computational Geometry, 1990 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Anders Björner +2 more
openaire +5 more sources
Electrical Networks, Hyperplane Arrangements and Matroids [PDF]
, 2019 This thesis introduces a class of hyperplane arrangements, called Dirichlet arrangements, arising from electrical networks with Dirichlet boundary conditions.
Lutz, Robert
core +7 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 +4 more sources
Combinatorial Depth Measures for Hyperplane Arrangements [PDF]
, 2023 Regression depth, introduced by Rousseeuw and Hubert in 1999, is a notion that measures how good of a regression hyperplane a given query hyperplane is with respect to a set of data points.
Soberón, Pablo, Schnider, Patrick
core +2 more sources
Branched Polymers and Hyperplane Arrangements [PDF]
Discrete & Computational Geometry, 2013 We generalize the construction of connected branched polymers and the notion of the volume of the space of connected branched polymers studied by Brydges and Imbrie, and Kenyon and Winkler to any hyperplane arrangement A. The volume of the resulting configuration space of connected branched polymers associated to the hyperplane arrangement A is ...
Postnikov, Alexander, Meszaros, Karola
openaire +6 more sources