Incidences Between Planes Over Finite Fields

In this note, we use methods from spectral graph theory to obtain bounds on the number of incidences between k-planes and h-planes in F-q(d), which generalizes a recent result given by Bennett, Iosevich, and Pakianathan (2014). More precisely, we prove that the number of incidences between a set K of k-planes and a set H of h-planes with h >= 2k + 1, which is denoted by I(K, H), satisfies