The Number of Crossing Free Configurations on Finite Point Sets in the Plane

2006 ◽  
pp. 20-20
Author(s):  
Emo Welzl
Keyword(s):  
Point Sets ◽  
Finite Point

Approximation by Exponential-Polynomial Products on Finite Point Sets

1972 ◽  
Vol 10 (1) ◽  
pp. 125-127 ◽  
Author(s):  
CHARLES B. DUNHAM
Keyword(s):  
Exponential Polynomial ◽  
Point Sets ◽  
Finite Point

Borsuk’s partition problem and finite point sets

2018 ◽  
Vol 59 (4) ◽  
pp. 709-716
Author(s):  
Theo Grundhöfer
Keyword(s):  
Partition Problem ◽  
Point Sets ◽  
Finite Point

scholarly journals Finite point-sets on S2 with minimum distance as large as possible

1986 ◽  
Vol 60 ◽  
pp. 3-66 ◽  
Author(s):  
L. Danzer
Keyword(s):  
Minimum Distance ◽  
Point Sets ◽  
Finite Point

Most Finite Point Sets in the Plane have Dilation $$>1$$ > 1

2014 ◽  
Vol 53 (1) ◽  
pp. 80-106 ◽  
Author(s):  
Rolf Klein ◽  
Martin Kutz ◽  
Rainer Penninger
Keyword(s):  
Point Sets ◽  
Finite Point

Matching algorithms for finite point sets in plane

2002 ◽  
Author(s):  
N.S.V. Rao ◽  
W. Wu ◽  
C.W. Glover
Keyword(s):  
Point Sets ◽  
Finite Point

Point Sets and Dynamical Systems In the Autocorrelation Topology

2004 ◽  
Vol 47 (1) ◽  
pp. 82-99 ◽  
Author(s):  
Robert V. Moody ◽  
Nicolae Strungaru
Keyword(s):  
Dynamical System ◽  
Point Sets ◽  
Finite Point ◽  
Locally Finite ◽  
Uniform Topology ◽  
Regular Model ◽  
Model Sets ◽  
Project Scheme ◽  
Compact Abelian Groups ◽  
Delone Sets

AbstractThis paper is about the topologies arising from statistical coincidence on locally finite point sets in locally compact Abelian groupsG. The first part defines a uniform topology (autocorrelation topology) and proves that, in effect, the set of all locally finite subsets ofGis complete in this topology. Notions of statistical relative denseness, statistical uniform discreteness, and statistical Delone sets are introduced.The second part looks at the consequences of mixing the original and autocorrelation topologies, which together produce a new Abelian group, the autocorrelation group. In particular the relation between its compactness (which leads then to aG-dynamical system) and pure point diffractivity is considered. Finally for generic regular model sets it is shown that the autocorrelation group can be identified with the associated compact group of the cut and project scheme that defines it. For such a set the autocorrelation group, as aG-dynamical system, is a factor of the dynamical local hull.

On the Geometric Dilation of Finite Point Sets

2003 ◽  
pp. 250-259 ◽  
Author(s):  
Annette Ebbers-Baumann ◽  
Ansgar Grüne ◽  
Rolf Klein
Keyword(s):  
Point Sets ◽  
Finite Point

scholarly journals Discrepancy, separation and Riesz energy of finite point sets on the unit sphere

2011 ◽  
Vol 39 (1) ◽  
pp. 27-43 ◽  
Author(s):  
Paul Leopardi
Keyword(s):  
Unit Sphere ◽  
Point Sets ◽  
Finite Point ◽  
Riesz Energy

scholarly journals Geometry without topology as a new conception of geometry

2002 ◽  
Vol 30 (12) ◽  
pp. 733-760 ◽  
Author(s):  
Yuri A. Rylov
Keyword(s):  
Riemannian Geometry ◽  
Space Region ◽  
Convex Region ◽  
Point Sets ◽  
Finite Point ◽  
Metric Tensor ◽  
Absolute Parallelism ◽  
Geometric Concepts ◽  
Metric Distance

A geometric conception is a method of a geometry construction. The Riemannian geometric conception and a new T-geometric one are considered. T-geometry is built only on the basis of information included in the metric (distance between two points). Such geometric concepts as dimension, manifold, metric tensor, curve are fundamental in the Riemannian conception of geometry, and they are derivative in the T-geometric one. T-geometry is the simplest geometric conception (essentially, only finite point sets are investigated) and simultaneously, it is the most general one. It is insensitive to the space continuity and has a new property: the nondegeneracy. Fitting the T-geometry metric with the metric tensor of Riemannian geometry, we can compare geometries, constructed on the basis of different conceptions. The comparison shows that along with similarity (the same system of geodesics, the same metric) there is a difference. There is an absolute parallelism in T-geometry, but it is absent in the Riemannian geometry. In T-geometry, any space region is isometrically embeddable in the space, whereas in Riemannian geometry only convex region is isometrically embeddable. T-geometric conception appears to be more consistent logically, than the Riemannian one.

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