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arXiv · 2606.14310

Residue Restrictions for a Two-Color Partition Series

Aman Singh
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Abstract

We study residue restrictions for a two-color partition series $P(q)=(q^4;q^4)_\infty S(q)$ arising from work of Andrews and Bachraoui on partitions with odd smallest part. Motivated by the explicit exponent structure in the Bailey-transform formulas for the associated generating function, we obtain elementary restrictions on the support of the coefficients. In particular, we show that the residue class $4\pmod8$ does not occur, and we prove a further refinement modulo $16$, yielding several vanishing classes for the coefficients of the series. Our argument is completely residue-theoretic and avoids the use of modular completions.

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Aman Singh. 2026-06-12. Residue Restrictions for a Two-Color Partition Series. https://arxiv.org/abs/2606.14310

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