Abstract
An explicit bijection is constructed between partitions of a positive integer n with exactly j even parts which are all different, and bipartitions (π 1; π 2) of n into distinct parts such that l( π 2)= j and max π 2⩽ l( π 1); this implies an identity due to Lebesgue. The construction is inspired by a version of Sylvester's bijective proof of Euler's identity using the 2-modular MacMahon diagram. This version and its generalization easily imply a number of refinements of Euler's, respectively, Lebesgue's identity.
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