Combinatorial proofs of two theorems related to the number of even parts in all partitions of n into distinct parts
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Recently, Andrews and Merca considered the number of even parts in all partitions of n into distinct parts and obtained new combinatorial interpretations for this number. Their proofs rely on generating functions. In this paper, we provide purely combinatorial proofs of these results.
Mathematics Subject Classification05A17 11P83
We are thankful to an anonymous referee for suggesting a clarification of one of the proofs.