Linear identities for partition pairs with $5$-cores

Russelle Guadalupe

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arXiv · 2601.04743

Linear identities for partition pairs with $5$-cores

Russelle Guadalupe

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Abstract

We prove an infinite family of linear identities for the number $A_5(n)$ of partition pairs of $n$ with $5$-cores by using certain theta function identities involving the Ramanujan's parameter $k(q)$ due to Cooper, and Lee and Park. Consequently, we deduce an infinite family of congruences for $A_5(n)$ using these linear identities.

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Russelle Guadalupe. 2026-01-08. Linear identities for partition pairs with $5$-cores. https://arxiv.org/abs/2601.04743

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