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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 $λ=(λ_1, λ_2, \ldots, λ_k)$ defined by $\mathrm{sp}(λ, x)=\prod_{i=1}^k(1+x^{λ_i})$. We study the sum of reciprocals of $\mathrm{sp}(λ, x)$ 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. 2026-06-08. Reciprocals of Subsum Polynomials. https://arxiv.org/abs/2605.10512

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