Combinatorial meaning of the number of the even parts in a partition of $n$ into distinct parts

Abstract

In a recent paper, Andrews and Merca investigated the number of even parts in all partitions of $n$ into distinct parts, which arise naturally from the Euler-Glaisher bijective proof. They obtained new combinatorial interpretations for this number by using generating functions. We obtain a new direct combinatorial proof in this note.

5 pages