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.
Core partitions with distinct parts
On the Polynomiality of moments of sizes for random $(n, dn\pm 1)$-core partitions with distinct parts
Explicit expressions for the moments of the size of an (n, dn-1)-core partition with distinct parts
![QR code for arXiv:2207.03661 [math.CO]](http://oss.arxitics.com/images/favicon.svg)