scholarly journals Integral Geometry in Projective and Affine Spaces

1950 ◽  
Vol 51 (3) ◽  
pp. 739 ◽  
Author(s):  
L. A. Santalo
Keyword(s):  
Integral Geometry ◽  
Affine Spaces ◽  
Projective And Affine Spaces

Blocking-sets in infinite projective and affine spaces

1987 ◽  
Vol 28 (2) ◽  
pp. 111-116 ◽  
Author(s):  
Albrecht Beutelspacher ◽  
Francesco Mazzocca
Keyword(s):  
Blocking Sets ◽  
Affine Spaces ◽  
Projective And Affine Spaces

Designs having the parameters of projective and affine spaces

2010 ◽  
Vol 60 (3) ◽  
pp. 225-240 ◽  
Author(s):  
D. M. Donovan ◽  
M. J. Grannell
Keyword(s):  
Affine Spaces ◽  
Projective And Affine Spaces

Projective and Affine Spaces

2013 ◽  
pp. 253-304
Author(s):  
Francis Buekenhout ◽  
Arjeh M. Cohen
Keyword(s):  
Affine Spaces ◽  
Projective And Affine Spaces

scholarly journals Characterizations of Finite Projective and Affine Spaces

1969 ◽  
Vol 21 ◽  
pp. 64-75 ◽  
Author(s):  
William M. Kantor
Keyword(s):  
Affine Space ◽  
Incidence Structure ◽  
Principal Result ◽  
List Type ◽  
Affine Spaces ◽  
Finite Projective Spaces ◽  
Finite Incidence ◽  
Finite Incidence Structure ◽  
Positive Integers ◽  
Projective And Affine Spaces

A well-known result of Dembowski and Wagner (4) characterizes the designs of points and hyperplanes of finite projective spaces among all symmetric designs. By passing to a dual situation and approaching this idea from a different direction, we shall obtain common characterizations of finite projective and affine spaces. Our principal result is the following.Theorem 1.A finite incidence structure is isomorphic to the design of points and hyperplanes of a finite projective or affine space of dimension greater than or equal to4if and only if there are positive integers v, k, and y, with μ> 1and(μ– l)(v — k) ≠ (k—μ)2such that the following assumptions hold.(I)Every block is on k points, and every two intersecting blocks are on μ common points.(II)Given a point and two distinct blocks, there is a block containing both the point and the intersection of the blocks.(III)Given two distinct points p and q, there is a block on p but not on q.(IV)There are v points, and v– 2 ≧k>μ.

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