Results 11 to 20 of about 3,366,340 (357)

On the finite field cone restriction conjecture in four dimensions and applications in incidence geometry [PDF]

arXiv, 2020
The first purpose of this paper is to solve completely the finite field cone restriction conjecture in four dimensions with $-1$ non-square. The second is to introduce a new approach to study incidence problems via restriction theory. More precisely, using the cone restriction estimates, we will prove sharp point-sphere incidence bounds associated with
Doowon Koh, Sujin Lee, T. Pham
arxiv   +3 more sources

Incidence geometry and universality in the tropical plane [PDF]

Journal of Combinatorial Theory, Series A, 2018
We examine the incidence geometry of lines in the tropical plane. We prove tropical analogs of the Sylvester-Gallai and Motzkin-Rabin theorems in classical incidence geometry.
Brandt, Milo, Jones, Michelle, Lee, Catherine, Ranganathan, Dhruv   +3 more
core   +2 more sources

Point-hyperplane Incidence Geometry and the Log-rank Conjecture [PDF]

ACM Transactions on Computation Theory, 2022
We study the log-rank conjecture from the perspective of point-hyperplane incidence geometry. We formulate the following conjecture: Given a point set in ℝd that is covered by constant-sized sets of parallel hyperplanes, there exists an affine subspace ...
Noah Singer, Madhu Sudan
openalex   +3 more sources

Regular Incidence Complexes, Polytopes, and C-Groups [PDF]

arXiv, 2017
Regular incidence complexes are combinatorial incidence structures generalizing regular convex polytopes, regular complex polytopes, various types of incidence geometries, and many other highly symmetric objects. The special case of abstract regular polytopes has been well-studied.
A Pasini, AC Duke, B Grünbaum, B Monson, B Monson, B Monson, Branko Grünbaum, D Pellicer, D Pellicer, D Pellicer, E Schulte, E Schulte, E Schulte, E Schulte, E Schulte, E Schulte, E. Schulte, F Buekenhout, F Buekenhout, F Buekenhout, G Cunningham, GC Shephard, HSM Coxeter, HSM Coxeter, HSM Coxeter, J. Tits, JE Humphreys, L Danzer, L. Danzer, M Aschbacher, M Aschbacher, MI Hartley, P McMullen, P McMullen, P McMullen, RC Lyndon, Richard P. Stanley, RM Weiss   +37 more
arxiv   +3 more sources

Convex subspaces of Lie incidence geometries [PDF]

Combinatorial Theory, 2022
We classify the convex subspaces of all hexagonic Lie incidence geometries (among which all long root geometries of spherical Tits-buildings). We perform a similar classification for most other Lie incidence geometries of spherical Tits-buildings, in particular for all projective and polar Grassmannians, and for exceptional Grassmannians of diameter at
Jeroen Meulewaeter, Hendrik Van Maldeghem   +1 more
openalex   +3 more sources

Coherent Magnetization Rotation of a Layered System Observed by Polarized Neutron Scattering under Grazing Incidence Geometry

Crystals, 2019
The in-plane magnetic structure of a layered system composed of polycrystalline grains smaller than the ferromagnetic exchange length was studied to elucidate the mechanism controlling the magnetic properties considerably different from the bulk using ...
Ryuji Maruyama, Thierry Bigault, Thomas Saerbeck, Dirk Honecker, Kazuhiko Soyama, Pierre Courtois   +5 more
doaj   +2 more sources

Matroid Enumeration for Incidence Geometry [PDF]

Discrete & Computational Geometry, 2011
Matroids are combinatorial abstractions for point configurations and hyperplane arrangements, which are fundamental objects in discrete geometry. Matroids merely encode incidence information of geometric configurations such as collinearity or coplanarity, but they are still enough to describe many problems in discrete geometry, which are called ...
David Bremner, Yoshitake Matsumoto, Sonoko Moriyama, Hiroshi Imai   +3 more
openaire   +2 more sources

Two cryptomorphic formalizations of projective incidence geometry [PDF]

Annals of Mathematics and Artificial Intelligence, 2018
Incidence geometry is a well-established theory which captures the very basic properties of all geometries in terms of points belonging to lines, planes, etc. Moreover, projective incidence geometry leads to a simple framework where many properties can be studied. In this article, we consider two very different but complementary mathematical approaches
Braun, David, Magaud, Nicolas, Schreck, Pascal   +2 more
openaire   +5 more sources

An axiom system for incidence spatial geometry

Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, 2008
Incidence spatial geometry is based on three-sorted structures consisting of points, lines and planes together with three intersort binary relations between points and lines, lines and planes and points and planes. We introduce an equivalent one-sorted geometrical structure, called incidence spatial frame, which is suitable for modal considerations. We
Alfonso Ríder Moyano, Rafael M. Rubio
openalex   +4 more sources

An Incidence Geometry approach to Dictionary Learning [PDF]

, 2015
We study the Dictionary Learning (aka Sparse Coding) problem of obtaining a sparse representation of data points, by learning \emph{dictionary vectors} upon which the data points can be written as sparse linear combinations.
Sitharam, Meera, Tarifi, Mohamad, Wang, Menghan   +2 more
core   +2 more sources