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Reciprocals of Subsum Polynomials

· 2026 · math.NT · arXiv 2605.10512

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abstract

We introduce the subsum polynomial of a partition $\lambda=(\lambda_1, \lambda_2, \ldots, \lambda_k)$ defined by $\mathrm{sp}(\lambda, x)=\prod_{i=1}^k(1+x^{\lambda_i})$. We study the sum of reciprocals of $\mathrm{sp}(\lambda, x)$ over all partitions of $n$. We prove arithmetic properties of related polynomials and offer connections to other combinatorial objects.

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Reciprocals of Partition Polynomials

math.CO · 2026-05-20 · accept · novelty 7.0 · 2 refs

Proves six conjectures on reciprocals of partition subsum polynomials via Lean formalizations while correcting one statement.

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  • Reciprocals of Partition Polynomials math.CO · 2026-05-20 · accept · full · ref 2 · 2 links · internal anchor

    Proves six conjectures on reciprocals of partition subsum polynomials via Lean formalizations while correcting one statement.