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Divisible Semiplanes

Authored by: Rudolf Mathon

Handbook of Combinatorial Designs

Print publication date:  November  2006
Online publication date:  November  2006

Print ISBN: 9781584885061
eBook ISBN: 9781420010541
Adobe ISBN:

10.1201/9781420010541-102

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Abstract

3.1

A divisible semiplane (or elliptic semiplane) S is a set of points P , a set of lines L , and an incidence relation beteween P and L such that:

Every line is incident with k points, and dually, every point is incident with k lines.

Any two distinct points are incident with at most one line, and dually, any two distinct lines have at most one point in common.

If a point p and a line L are not incident, then there exists at most one line incident with p and parallel to L, and dually, there exists at most one point incident with L and noncollinear with p.

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