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Launched on June 11, 2008, the LAT instrument onboard the $Fermi$ Gamma-raySpace Telescope has provided a rare opportunity to study high energy photonemission from gamma-ray bursts. Although the majority of such events (27) havebeen iden tified by the Fermi LAT Collaboration, four were uncovered by usingmore 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 findingthree more GRBs ass ociated with high energy photon emission, GRB 110709A,7A and 120107A. To s ystematize our matched filter approach, a pipelinehas been developed to identif y these objects in near real time. GRB 120107A isthe first product of this anal ysis procedure. Despite the reduced thresholdfor identification, the number of GRB events has not increased significantly.This relative dearth of events with low photon number prompted a study of theapparent photon number distribution. W e find an extremely good fit to a simplepower-law with an exponent of -1.8 $\pm $ 0.3 for the differentialdistribution. As might be expected, there is a substa ntial correlation betweenthe number of lower energy photons detected by the GBM and the number observedby the LAT. Thus, high energy photon emission is associ ated with some but notall of the brighter GBM events. Deeper studies of the pro perties of the smallpopulation of high energy emitting bursts may eventually yi eld a betterunderstanding of these entire phenomena.

GRB 110709A, 111117A and 120107A: Faint high-energy gamma-ray photon emission from Fermi/LAT observations and demographic implications