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JCT
2007

Weighted forms of Euler's theorem

9 years 6 months ago
Weighted forms of Euler's theorem
In answer to a question of Andrews about finding combinatorial proofs of two identities in Ramanujan’s “lost” notebook, we obtain weighted forms of Euler’s theorem on partitions with odd parts and distinct parts. This work is inspired by the insight of Andrews on the connection between Ramanujan’s identities and Euler’s theorem. Our combinatorial formulations of Ramanujan’s identities rely on the notion of rooted partitions. Pak’s iterated Dyson’s map and Sylvester’s fish-hook bijection are the main ingredients in the weighted forms of Euler’s theorem.
William Y. C. Chen, Kathy Q. Ji
Added 27 Dec 2010
Updated 27 Dec 2010
Type Journal
Year 2007
Where JCT
Authors William Y. C. Chen, Kathy Q. Ji
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