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arXiv · 2410.17378

A generalization of Franklin's partition identity and a Beck-type companion identity

Gabriel Gray·David Hovey·Brandt Kronholm·Emily Payne·Holly Swisher·Ren Watson
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Abstract

Euler's classic partition identity states that the number of partitions of $n$ into odd parts equals the number of partitions of $n$ into distinct parts. We develop a new generalization of this identity, which yields a previous generalization of Franklin as a special case, and prove an accompanying Beck-type companion identity.

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Gabriel Gray, David Hovey, Brandt Kronholm, Emily Payne, Holly Swisher, Ren Watson. 2024-10-22. A generalization of Franklin's partition identity and a Beck-type companion identity. https://arxiv.org/abs/2410.17378

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