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We look at extensions of formulas given by Jovovic and recently proved byDhar on integer partitions where the smallest part occurs at least $m$ timesand on integer partitions with fixed differences between the largest andsmallest parts where the smallest part occurs at least $k$ times. Our resultsextend Dhar's results for the $m=2$ and $k=1$ cases to the general cases forarbitrary $m$ and $k$. We also look at analogous results for overpartitions and$\ell$-regular partitions.

Extensions of some results of Jovovic and Dhar