Shiwei Cao, Jing Jin, Olivia X. M. Yao, Xinyuan Zhou: Infinite families of congruences modulo 4 for 16-regular partitions, 219-229

Abstract:

Let $b_t(n)$ denote the number of $t$-regular partitions of $n$. In recent years, some parities for $b_t(n)$ have been proved for small $t$. In particular, some infinite families of congruences modulo 2 for $b_{16}(n)$ were established by Cui and Gu. Motivated by their work, we prove several infinite families of congruences modulo 4 for $b_{16}(n)$.

Key Words: Regular partition, congruence, theta function identities.

2020 Mathematics Subject Classification: Primary 11P83; Secondary 05A17.

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