Parity results for 9-core and self-conjugate 9-core partitions
Volume 151 / 2018
Colloquium Mathematicum 151 (2018), 27-36 MSC: Primary 11P83; Secondary 05A17. DOI: 10.4064/cm6802-8-2016 Published online: 13 October 2017
Let $a_t(n)$ and $asc_t(n)$ denote the number of $t$-core partitions of $n$ and the number of self-conjugate $t$-core partitions of $n$, respectively. Some congruences for $a_t(n)$ and $asc_t(n)$ are known when $t$ is a prime or a power of 2. We establish several infinite families of congruences modulo 2 for $a_9(n)$ and $asc_9(n)$ by using the theory of quadratic residues and theta function identities.