Manickam-Miklós-Singhi Conjectures on Partial Geometries

Abstract

In this paper we give a proof of the Manickam-Miklós-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 counter-examples to the conjecture are described.

15 pages, accepted in DCC, corrected ordering of the Ms in MMS in title and abstract