A bijection for Lebesgue's partition identity in the spirit of Sylvester (Q1336644)

By analysing hooks in the 2-modular Ferrers diagrams of partitions, a combinatorial proof of a well-known identity due to Lebesgue is given. The explicit bijection constructed here goes along the lines of a correspondence set up by Sylvester in his classic paper on partitions of 1882. The method of the author not only leads to generalisations of the Euler-Sylvester identities on odd parts and distinct parts, but applies to the analogous situation given by \(p\)-modular diagrams.