Editing Incidence structure (section)

{{short description|Abstract mathematical system of two types of objects and a relation between them}}
[[File:Inzidenz-struktur.svg|thumb|Examples of incidence structures:<br />
Example 1: points and lines of the Euclidean plane (top)<br />
Example 2: points and circles (middle),<br />
Example 3: finite incidence structure defined by an [[incidence matrix]] (bottom)]]

In [[mathematics]], an '''incidence structure''' is an abstract system consisting of two types of objects and a single relationship between these types of objects. Consider the [[Point (geometry)|point]]s and [[Line (geometry)|line]]s of the [[Euclidean plane]] as the two types of objects and ignore all the properties of this geometry except for the [[heterogeneous relation|relation]] of which points are [[incident (geometry)|incident]] on which lines for all points and lines. What is left is the incidence structure of the Euclidean plane.

Incidence structures are most often considered in the geometrical context where they are abstracted from, and hence generalize, planes (such as [[affine plane (incidence geometry)|affine]], [[projective plane|projective]], and [[Möbius plane]]s), but the concept is very broad and not limited to geometric settings. Even in a geometric setting, incidence structures are not limited to just points and lines; higher-dimensional objects ([[Plane (mathematics)|plane]]s, [[Solid geometry|solid]]s, {{mvar|n}}-spaces, [[Conical surface|conics]], etc.) can be used. The study of finite structures is sometimes called [[finite geometry]].<ref>{{harvnb|Colbourn|Dinitz|2007|page=702}}</ref>