Applications of Fa\`{a} di Bruno's formula to partition traces
Number Theory
2025-07-02 v1 Combinatorics
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.
Cite
@article{arxiv.2507.00404,
title = {Applications of Fa\`{a} di Bruno's formula to partition traces},
author = {Toshiki Matsusaka},
journal= {arXiv preprint arXiv:2507.00404},
year = {2025}
}
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8 pages