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arXiv · 2605.10512

Reciprocals of Subsum Polynomials

Cristina Ballantine·George Beck·Brooke Feigon·Kathrin Maurischat
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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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Cristina Ballantine, George Beck, Brooke Feigon, Kathrin Maurischat. 2026-05-11. Reciprocals of Subsum Polynomials. https://arxiv.org/abs/2605.10512

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