Configuration (geometry) - Notation

Notation

A configuration in the plane is denoted by (p_γ ℓ_π), where p is the number of points, ℓ the number of lines, γ the number of lines per point, and π the number of points per line. These numbers necessarily satisfy the equation

as this product is the number of point-line incidences.

The notation (p_γ ℓ_π) does not determine a projective configuration up to incidence isomorphism. For instance, there exist three different (9₃ 9₃) configurations: the Pappus configuration and two less notable configurations.

In some configurations, p = ℓ and γ = π. These are called symmetric configurations and the notation is often condensed to avoid repetition. For example (9₃ 9₃) abbreviates to (9₃).