Results 281 to 290 of about 228,651 (326)

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
openaire   +3 more sources

Geometric Hyperplanes of Lie Incidence Geometries [PDF]

Geometriae Dedicata, 1997
Let \(\Gamma=({\mathcal P},{\mathcal L})\) be a geometry of points and lines. A subspace of \(\Gamma\) is a set of points which contains every line that meets it in at least two points. An embedding \(\mu\) of \(\Gamma\) in a finite-dimensional vector space \(V\) consists of a map \(\mu_1\) of \({\mathcal P}\) into the set of 1-subspaces of \(V\) and a
Bruce N. Cooperstein, Ernest E. Shult
openaire   +2 more sources

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.
openaire   +3 more sources

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
openaire   +3 more sources

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
openaire   +2 more sources

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
openaire   +2 more sources

FORMALIZATION OF HILBERT'S GEOMETRY OF INCIDENCE AND PARALLELISM

Synthese, 1997
The author first describes how \textit{D. Hilbert} changed the phrasing of his axioms of incidence in the various early editions of his Grundlagen der Geometrie [(Teubner, Leipzig) (1899; JFM 30.0424.01); second edition (1903; JFM 34.0523.01); seventh edition (1930; JFM 56.0481.01)], in which ``bestimmen'' gave way to ``es gibt''.
openaire   +3 more sources

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
openaire   +2 more sources

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
openaire   +2 more sources

Incidence loops and their geometry

1992
Publisher Summary This chapter discusses the concept of incidence loops and their geometry. An incidence group (P, L,·) is a group (P,·) together with a structure (P, L) of an incidence space such that both structures are compatible. The notion of incidence group can be generalized by weakening the assumptions concerning the algebraic structure of P;
openaire   +2 more sources