Linear identities for partition pairs with 4-cores

Russelle Guadalupe

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arXiv · 2601.10438

Linear identities for partition pairs with 4-cores

Russelle Guadalupe

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Abstract

We determine an infinite family of linear identities for the number $A_4(n)$ of partition pairs of $n$ with $4$-cores by employing elementary $q$-series techniques and certain $3$-dissection formulas. We then discover an infinite family of congruences for $A_4(n)$ as a consequence of these linear identities.

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Russelle Guadalupe. 2026-01-15. Linear identities for partition pairs with 4-cores. https://arxiv.org/abs/2601.10438

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