Sparsity conditions on combinatorial structures are fundamental in rigidity theory. In some situations, for instance when considering scenes and parallel redrawings, the relevant sparsity condition is on the incidences of a rank two incidence geometry.

In this talk, we define sparsity and tightness of rank 2 incidence geometries, and we develop an algorithm which recognises these properties. Furthermore, under certain conditions, this algorithm also allows us to find a maximum size tight subgeometry. This work builds on existing pebble game algorithms for graphs and hypergraphs. The main difference compared to the previously studied hypergraph case is that in this paper, the sparsity and tightness are defined in terms of incidences, and not in terms of edges.

This talk is based on joint work with Tovohery H. Randrianarisoa, Klara Stokes and Joannes Vermant.