Weighted Forms of Euler's Theorem

Details Weighted Forms of Euler's Theorem Weighted Forms of Euler's Theorem

2005-10-06

arxiv.org/abs/math/0510121v1

Mathematics

Combinatorics

14 pages

Scientific paper

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. Iterated Dyson's map and Sylvester's bijection are the main ingredients in the weighted forms of Euler's theorem.

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