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A generalization of Franklin's partition identity and a Beck-type companion identity (2410.17378v1)
Published 22 Oct 2024 in math.NT and math.CO
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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