Incidence structure

In mathematics, in particular in combinatorics, an incidence structure is a triple

<math>C=(P,L,I)<math>

where <math>P<math> is the set of "points", <math>L<math> is the set of "lines" and <math>I \subseteq P \times L<math> is the incidence relation. The elements of <math>I<math> are called flags. If <math>(p,l) \in L<math> we say that "point" <math>p<math> lies on "line" <math>l<math>.

Each hypergraph or set system can be regarded as an incidence structure in which the universal set plays the role of "points", the corresponding family of sets plays the role of "lines" and the incidence relation is given by <math>\in<math>.

In particular, let

P = {1,2,3,4,5,6,7},

L = {{1,2,4},{2,3,5},{3,4,6},{4,5,7},{5,6,1},{6,7,2},{7,1,3}}

<math>I = \in<math>.

The corresponding incidence structure is called the Fano plane.

See also: incidence (geometry).