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May 10, 2010 at 21:50 comment added Igor Pak Huh? I don't follow. Euler did not have "bijective proof" as a concept. It was Glaisher who invented the bijection, but if I recall correctly never published it - Sylvester did it and attributed it to him some time later. You are probably referring to Euler's "odd vs. distinct" partitions theorem. Using modern "involution principle" technology one can convert analytic proofs into bijective, and in this case the one-line Euler's proof becomes Glaisher's bijection (this is O'Hara's theorem - see my survey on partitions and a recent paper on O'Hara algorithm, joint with Konvalinka).
May 10, 2010 at 20:08 history answered Harrison Brown CC BY-SA 2.5