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In 2015, Bringmann, Lovejoy and Mahlburg considered certain kindsoverpartitions, which can been seen as the overpartition analogue of Schur'spartition. The motivation of their work is that the difference between thegenerating function of Schur's classical partitions and the generatingfunctions of the partitions in which the smallest part is excluded. Thedifference between the two generating functions of partitions is aspecialization of the "universal" mock theta function g_3 which introduced byHickerson. To give an analogue of this, by using another universal mock thetafunction g_2 instead of g_3, Bringmann Lovejoy and Mahlburg introduced twokinds of overpartitions, which satisfy certain congruence conditions anddifference conditions with the smallest parts different. They prove thesetheorems by using the q-differential equations. In this paper, we will give thegenerating functions of these two kinds of overpartitions by combinatorialtechnique.

Combinatorial Proofs of Two Overpartition Theorems Connected by a Universal Mock Theta Function