The combinatorics of identities involving overpartitions with distinct parts

Abstract

Recently, Andrews and EI Bachraoui discovered several companions for some famous $q$-series formulas, and derived some new identities involving partitions and overpartitions with distinct parts. In this paper, we shall refine their results by the number of parts of partitions and furthermore, we will also provide the combinatorial proofs for those partition identities.

14 pages