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arXiv · 2407.15628

A note on congruences for generalized cubic partitions modulo primes

Russelle Guadalupe
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Abstract

Recently, Amdeberhan, Sellers, and Singh introduced the notion of a generalized cubic partition function $a_c(n)$ and proved two isolated congruences via modular forms, namely, $a_3(7n+4)\equiv 0\pmod{7}$ and $a_5(11n+10)\equiv 0\pmod{11}$. In this paper, we provide another proof of these congruences by using classical $q$-series manipulations. We also give infinite families of congruences for $a_c(n)$ for primes $p\not\equiv 1\pmod{8}$.

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Russelle Guadalupe. 2024-07-22. A note on congruences for generalized cubic partitions modulo primes. https://doi.org/10.5281/zenodo.14907350

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