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On perspectivities in incidence geometries of grade n

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On the foundations of incidence geometry

Geometriae Dedicata, 1988
Diagram geometries and chamber systems of various types have been used and investigated intensively in recent years - not only in finite group theory, but in other areas as well. This development has led to a need for some clarification of the variations and generalizations introduced by the many authors, and for a discussion of the different axiomatic
Buekenhout, Francis, Buset, Dominique
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On the incidence geometry of Grassmann spaces

Geometriae Dedicata, 1999
The main result is a characterization of the Grassmann space \({\mathbf G}\) of a projective space \(\mathcal P\). By definition, the point set \(P\) of \({\mathbf G}\) is the set of lines of \(\mathcal P\), the line set \(\mathcal L\) of \({\mathbf G}\) consists of all plane line pencils in \(\mathcal P\).
FERRARA DENTICE, Eva, MELONE N.
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Modal logics for incidence geometries

Journal of Logic and Computation, 1997
Let \(S=(P,L,\text{in})\) be an incidence plane by the well-known axioms: \(P,L\neq\emptyset\); \(\text{in}\subseteq P\times L\); \(P\cap L=\emptyset\); two points are together incident with one and only one line; each line contains at least two different points; each point belongs at least to two different lines.
Balbiani, Philippe, Fariñas del Cerro, Luis, Tinchev, Tinko, Vakarelov, Dimiter   +3 more
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Incidence and Metric Geometry

1981
In this section we shall define the notions of an abstract geometry and an incidence geometry. These are given by listing a set of axioms that must be satisfied. After the definitions are made, we will give a number of examples which will serve as models for these geometries.
George D. Parker, Richard S. Millman
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Frames and bases of Lie incidence geometries

Journal of Geometry, 1997
The authors consider Lie incidence geometries \(\Gamma=({\mathcal P},{\mathcal L})\) of types \(B_{n,n}\) and \(C_{n,1}\) over a field of characteristic not two, \(A_{n,k}\), \(D_{n,1}\), \(D_{n,n}\), \(E_{6,1}\) or \(E_{7,1}\) and show that a subset \(X\subset {\mathcal P}\) is an apartment of \(\Gamma\) if and only if one of the following conditions ...
Bruce N. Cooperstein, Bruce N. Cooperstein, Ernest E. Shult, Ernest E. Shult   +3 more
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Implicit characterizations of smooth incidence geometries

Geometriae Dedicata, 2000
Erworben im Rahmen der Schweizer Nationallizenzen (http://www.nationallizenzen.ch)
Richard Bödi, Stefan Immervoll
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Preliminaries and Incidence Geometry (I)

2015
This chapter contains a brief summary of several types of mathematical knowledge needed to read this book, including the elements of logic, set theory, mapping theory, and algebraic structures such as number systems and vector spaces. Definitions of basis, dimension, linear mappings, isomorphism, matrices and determinants are given; there is also ...
Keith G. Calkins, Harold Trainer Jones, Donald H. Rhoads, Edward John Specht   +3 more
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Two incidence propositions in chain geometries

Monatshefte für Mathematik, 2011
The significance of the incidence propositions (Z) and (B) for chain geometries Σ(F, A, J) is determined. In preparation the structure of kinematic and nearquadratic Jordan systems is studied.
Münevver Özcan, Armin Herzer
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Darwin's theory for the grazing incidence geometry

Surface Science, 2001
Darwin's dynamical theory of X-ray diffraction was studied in the case of grazing incidence geometry. It was shown that in such geometry the Darwin theory is not correct. In the two-beam case, the reflectivity of the specular reflection calculated by the original Darwin's theory was slightly different from that calculated by the well-known Fresnel ...
Toshio Takahashi, M. Takahasi, Y. Ito, Wataru Yashiro   +3 more
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