MIKL´ OS-MANICKAM-SINGHI CONJECTURES ON PARTIAL GEOMETRIES

Abstract

In this paper we give a proof of the Mikl´os-Manickam-Singhi (MMS) conjecture for some partial geometries. Specifically, we give a condition on partial geometries which implies that the MMS conjecture holds. Further, several specific partial geometries that are counterexamples to the conjecture are described.