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
Abstract
Let 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.