  Launched on June 11, 2008, the LAT instrument onboard the $Fermi$ Gamma-ray Space Telescope has provided a rare opportunity to study high energy photon emission from gamma-ray bursts. Although the majority of such events (27) have been iden tified by the Fermi LAT Collaboration, four were uncovered by using more sensiti ve statistical techniques (Akerlof et al 2010, Akerlof et al 2011, Zheng et al 2 012). In this paper, we continue our earlier work by finding three more GRBs ass ociated with high energy photon emission, GRB 110709A, 111117A and 120107A. To s ystematize our matched filter approach, a pipeline has been developed to identif y these objects in near real time. GRB 120107A is the first product of this anal ysis procedure. Despite the reduced threshold for identification, the number of GRB events has not increased significantly. This relative dearth of events with low photon number prompted a study of the apparent photon number distribution. W e find an extremely good fit to a simple power-law with an exponent of -1.8 $\pm $ 0.3 for the differential distribution. As might be expected, there is a substa ntial correlation between the number of lower energy photons detected by the GBM and the number observed by the LAT. Thus, high energy photon emission is associ ated with some but not all of the brighter GBM events. Deeper studies of the pro perties of the small population of high energy emitting bursts may eventually yi eld a better understanding of these entire phenomena. 
GRB 110709A, 111117A and 120107A: Faint high-energy gamma-ray photon   emission from Fermi/LAT observations and demographic implications