scholarly journals Intertwining automorphisms in finite incidence structures

1989 ◽  
Vol 117 ◽  
pp. 25-34 ◽  
Author(s):  
Alan Camina ◽  
Johannes Siemons
Keyword(s):  
Incidence Structures ◽  
Finite Incidence

scholarly journals BRUCK NETS AND PARTIAL SHERK PLANES

2017 ◽  
Vol 104 (1) ◽  
pp. 1-12
Author(s):  
JOHN BAMBERG ◽  
JOANNA B. FAWCETT ◽  
JESSE LANSDOWN
Keyword(s):  
Affine Plane ◽  
Finite Geometries ◽  
Affine Planes ◽  
Incidence Structures ◽  
Finite Affine ◽  
Odd Order ◽  
Finite Incidence ◽  
Desarguesian Affine Plane

In Bachmann [Aufbau der Geometrie aus dem Spiegelungsbegriff, Die Grundlehren der mathematischen Wissenschaften, Bd. XCVI (Springer, Berlin–Göttingen–Heidelberg, 1959)], it was shown that a finite metric plane is a Desarguesian affine plane of odd order equipped with a perpendicularity relation on lines and that the converse is also true. Sherk [‘Finite incidence structures with orthogonality’, Canad. J. Math.19 (1967), 1078–1083] generalised this result to characterise the finite affine planes of odd order by removing the ‘three reflections axioms’ from a metric plane. We show that one can obtain a larger class of natural finite geometries, the so-called Bruck nets of even degree, by weakening Sherk’s axioms to allow noncollinear points.

Colouring finite incidence structures

1986 ◽  
Vol 2 (1) ◽  
pp. 339-346 ◽  
Author(s):  
J. Csima ◽  
Z. Füredi
Keyword(s):  
Incidence Structures ◽  
Finite Incidence

An interactive program for finite incidence structures

1980 ◽  
Vol 14 (2) ◽  
pp. 174-181
Author(s):  
Marilena Barnabei ◽  
Giorgio Nicoletti
Keyword(s):  
Interactive Program ◽  
Incidence Structures ◽  
Finite Incidence

Finite Incidence Structures with Orthogonality

1967 ◽  
Vol 19 ◽  
pp. 1078-1083 ◽  
Author(s):  
F. A. Sherk
Keyword(s):  
Incidence Structure ◽  
Affine Planes ◽  
Axiom A ◽  
Incidence Structures ◽  
Finite Incidence

An incidence structure consists of two sets of elements, called points and blocks, together with a relation, called incidence, between elements of the two sets. Well-known examples are inversive planes, in which the blocks are circles, and projective and affine planes, in which the blocks are lines. Thus in various examples of incidence structures, the blocks may have various interpretations. Very shortly, however, we shall impose a condition (Axiom A) which ensures that the blocks behave like lines. In anticipation of this, we shall refer to the set of blocks as the set of lines. Also, we shall employ the usual terminology of incidence, such as “lies on,” “passes through,” “meet,” “join.” etc.

Uncovering antibody incidence structures

1980 ◽  
Vol 52 (1-2) ◽  
pp. 141-156 ◽  
Author(s):  
George Markowsky ◽  
Andrew Wohlgemuth
Keyword(s):  
Incidence Structures

scholarly journals Exploring Steinitz-Rademacher Polyhedra: a Challenge for Automated Reasoning Tools

10.29007/d3ls ◽  
2018 ◽  
Author(s):  
Jesse Alama
Keyword(s):  
Automated Reasoning ◽  
Order Theory ◽  
Incidence Structures ◽  
First Order ◽  
First Order Theory

This note reports on some experiments, using a handful of standard automated reasoning tools, for exploring Steinitz-Rademacher polyhedra, which are models of a certain first-order theory of incidence structures. This theory and its models, even simple ones, presents significant, geometrically fascinating challenges for automated reasoning tools are.

scholarly journals Incidence structures applied to cryptography

1992 ◽  
Vol 106-107 ◽  
pp. 383-389 ◽  
Author(s):  
Fred Piper ◽  
Peter Wild
Keyword(s):  
Incidence Structures
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