Sharp homogeneity in affine planes, and in some affine generalized polygons

2004 ◽  
Vol 74 (1) ◽  
pp. 163-174 ◽  
Author(s):  
T. Grundhöfer ◽  
H. Van Maldeghem
Keyword(s):  
Affine Planes ◽  
Generalized Polygons

Erdélyi–Kober fractional integrals and radon transforms for mutually orthogonal affine planes

2020 ◽  
Vol 23 (4) ◽  
pp. 967-979
Author(s):  
Boris Rubin ◽  
Yingzhan Wang
Keyword(s):  
Fractional Integrals ◽  
Radon Transforms ◽  
Affine Planes ◽  
Inversion Formulas ◽  
Radial Functions ◽  
Compactly Supported ◽  
Radial Case ◽  
Compactly Supported Functions

AbstractWe apply Erdélyi–Kober fractional integrals to the study of Radon type transforms that take functions on the Grassmannian of j-dimensional affine planes in ℝn to functions on a similar manifold of k-dimensional planes by integration over the set of all j-planes that meet a given k-plane at a right angle. We obtain explicit inversion formulas for these transforms in the class of radial functions under minimal assumptions for all admissible dimensions. The general (not necessarily radial) case, but for j + k = n − 1, n odd, was studied by S. Helgason [8] and F. Gonzalez [4, 5] on smooth compactly supported functions.

On order in generalized polygons

1981 ◽  
Vol 10 (1-4) ◽  
pp. 451-458 ◽  
Author(s):  
A. Yanushka
Keyword(s):  
Generalized Polygons

Geometry in affine planes

2019 ◽  
pp. 118-129
Author(s):  
E. Sernesi
Keyword(s):  
Affine Planes

scholarly journals Finite Geometric Spaces, Steiner Systems and Cooperative Games

2014 ◽  
Vol 22 (1) ◽  
pp. 189-205 ◽  
Author(s):  
Antonio Maturo ◽  
Fabrizio Maturo
Keyword(s):  
Cooperative Games ◽  
Steiner Systems ◽  
Affine Planes

AbstractSome relations between finite geometric spaces and cooperative games are considered. The games associated to Steiner systems, in particular projective and affine planes, are considered. The properties of winning and blocking coalitions are investigated.

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