منابع مشابه
Legitimate colorings of projective planes
For a projective plane Pn of order n, let X(Pn) denote the minimum number k, so that there is a coloring of the points of P~ in k colors such that no two distinct lines contain precisely the same number' of points of each color. Answering a question of A. Rosa, we show that for all sufficiently large n, 5 < X(Pn) < 8 for every projective plane P, of order n.
متن کاملProjective Planes of Type
During the last few years, there has been a mild surge of interest in projective planes of type I-4. This paper is intended to both provide a survey of some recent theorems, and to present some new results concerning these planes. In Section 2, we describe the algebraic setting for these planes. Special attention is given to the structure of the relevant homology groups. In Section 3, some rece...
متن کاملSmooth Projective Planes
Using symplectic topology and the Radon transform, we prove that smooth 4-dimensional projective planes are diffeomorphic to CP. We define the notion of a plane curve in a smooth projective plane, show that plane curves in high dimensional regular planes are lines, prove that homeomorphisms preserving plane curves are smooth collineations, and prove a variety of results analogous to the theory ...
متن کاملProjective Planes in Algebraically
We investigate the combinatorial geometry obtained from algebraic closure over a fixed subfield in an algebraically closed field. The main result classifies the subgeometries which are isomorphic to projective planes. This is applied to give new examples of algebraic characteristic sets of matroids. The main technique used, which is motivated by classical projective geometry, is that a particul...
متن کاملExtending Partial Projective Planes
If a finite partial projective plane can be extended to a projective plane of order n, then it can be extended by a sequence of one line extensions. We describe necessary conditions for such an extension to exist, and restrictions which can be imposed on the intermediate sequence of extensions. This method can be used to attempt to construct a projective plane of non-prime-power order. 1. Parti...
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ژورنال
عنوان ژورنال: Graphs and Combinatorics
سال: 1989
ISSN: 0911-0119,1435-5914
DOI: 10.1007/bf01788662