  In 2015, Bringmann, Lovejoy and Mahlburg considered certain kinds
overpartitions, which can been seen as the overpartition analogue of Schur's
partition. The motivation of their work is that the difference between the
generating function of Schur's classical partitions and the generating
functions of the partitions in which the smallest part is excluded. The
difference between the two generating functions of partitions is a
specialization of the "universal" mock theta function g_3 which introduced by
Hickerson. To give an analogue of this, by using another universal mock theta
function g_2 instead of g_3, Bringmann Lovejoy and Mahlburg introduced two
kinds of overpartitions, which satisfy certain congruence conditions and
difference conditions with the smallest parts different. They prove these
theorems by using the q-differential equations. In this paper, we will give the
generating functions of these two kinds of overpartitions by combinatorial
technique.
