Incidence structures

Related pages

Dual incidence structure
Incidence matrices
An incidence structure is a triple where and are two sets, called the set of points and lines, respectively. The final component I is a subset called the incidence relation. The relation means that the point p is on the line l.

Given a line l, the set

is the point row of the line l. Similarly, given a point p, the line pencil through p is defined to be

Note that a line l is not determined by its point row, but this is true in all incidence structures which are usually considered, for example in partial linear spaces.

The concept of an incidence structure is not really usefull for its own sake. It is used as a general setting to define more specific geometric structures.

See also

Contributed by Hauke Klein
Version $Id: incidence.html,v 1.4 2001/01/02 19:41:04 hauke Exp $