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arXiv · 2507.00404

Applications of Fa\`{a} di Bruno's formula to partition traces

Toshiki Matsusaka
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Abstract

We revisit several partition-theoretic generating functions, including the theta quotients from Ramanujan's lost notebook, MacMahon's partition functions, and reciprocal sums of parts in partitions, through the lens of the classical Fa\`{a} di Bruno formula. This approach offers a unified and natural reinterpretation of known results and provides a systematic framework for deriving new identities of a similar type.

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Toshiki Matsusaka. 2025-07-01. Applications of Fa\`{a} di Bruno's formula to partition traces. https://arxiv.org/abs/2507.00404

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