Arc (projective geometry)

The red points are a 4-arc in Fano plane, the projective plane of order 2.
For arcs in a real or complex projective space, see Arc (geometry).

A (simple) arc in finite projective geometry is a set of points which satisfies, in an intuitive way, a feature of curved figures in continuous geometries. Loosely speaking, they are sets of points that are far from "line-like" in a plane or far from "plane-like" in a three-dimensional space. In this finite setting it is typical to include the number of points in the set in the name, so these simple arcs are called k-arcs. An important generalization of k-arcs, also referred to as arcs in the literature, is the (k, d)-arcs.