Results 11 to 20 of about 224,319 (283)
FinInG: a package for Finite Incidence Geometry
, 2016 FinInG is a package for computation in Finite Incidence Geometry. It provides users with the basic tools to work in various areas of finite geometry from the realms of projective spaces to the flat lands of generalised polygons. The algebraic power of GAP is exploited, particularly in its facility with matrix and permutation groups.
John Bamberg +5 more
openalex +4 more sources
Quotients of incidence geometries [PDF]
Designs, Codes and Cryptography, 2011 We develop a theory for quotients of geometries and obtain sufficient conditions for the quotient of a geometry to be a geometry. These conditions are compared with earlier work on quotients, in particular by Pasini and Tits. We also explore geometric properties such as connectivity, firmness and transitivity conditions to determine when they are ...
Cara, Philippe +3 more
openaire +5 more sources
Point-curve incidences in the complex plane [PDF]
, 2017 We prove an incidence theorem for points and curves in the complex plane. Given a set of $m$ points in ${\mathbb R}^2$ and a set of $n$ curves with $k$ degrees of freedom, Pach and Sharir proved that the number of point-curve incidences is $O\big(m ...
Sheffer, Adam +2 more
core +2 more sources
THE FULFILLED EUCLIDEAN PLANE [PDF]
, 2009 The fulfilled euclidean plane is the real projective plane, completed with the infinite point of its infinite line denoted new incidence structure. This is a structure with neighbouring elements, in which the unicity of the line through two distinct ...
Vasiu, Adrian, Vasiu, Angela
core +1 more source
Incidences between points and lines in three dimensions [PDF]
, 2015 We give a fairly elementary and simple proof that shows that the number of incidences between $m$ points and $n$ lines in ${\mathbb R}^3$, so that no plane contains more than $s$ lines, is $$ O\left(m^{1/2}n^{3/4}+ m^{2/3}n^{1/3}s^{1/3} + m + n\right) $$
Sharir, Micha, Solomon, Noam
core +3 more sources
High efficiency near diffraction-limited mid-infrared flat lenses based on metasurface reflectarrays [PDF]
, 2016 A limiting factor in the development of mid-infrared optics is the lack of abundant materials that are transparent, low cost, lightweight, and easy to machine. In this paper, we demonstrate a metasurface device that circumvents these limitations.
Aieta, Francesco +11 more
core +3 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 +3 more
openaire +1 more source
Regular Incidence Complexes, Polytopes, and C-Groups
, 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.
A Pasini +37 more
core +1 more source
The classification of flag-transitive Steiner 3-designs
, 2004 We solve the long-standing open problem of classifying all 3-(v,k,1) designs with a flag-transitive group of automorphisms (cf. A. Delandtsheer, Geom. Dedicata 41 (1992), p. 147; and in: "Handbook of Incidence Geometry", ed. by F.
Huber, Michael
core +1 more source
Light propagation in atomic Mott Insulators [PDF]
, 2008 We study radiation-matter interaction in a system of ultracold atoms trapped in an optical lattice in a Mott insulator phase. We develop a fully general quantum model, and we perform calculations for a one-dimensional geometry at normal incidence.
Adams +37 more
core +3 more sources