  In this article, we study the localizaiton of the partition function of BPS
vortices in $\mathcal{N}=(2,2)$ $U(N)$ super Yang-Mills theory with $N$-flavor
on $\R^2$. The vortex partition function for $\mathcal{N}=(2,2)$ super
Yang-Mills theory is obtained from the one in $\mathcal{N}=(4,4)$ super
Yang-Mills theory by mass deformation. We show that the partition function can
be written as $Q$-exact form and integration in the partition functions is
localized to the fixed points which are related to $N$-tuple one dimensional
partitions of positive integers.
