New Congruences Modulo 3 for 11-Core Partition Function
If tis a positive integer, then a partition of a nonnegative integern is a t-core if none of the hook numbers of the associated Ferrers-Young diagram is a multiple of t. These partitions play important roles in the study of irreducible representations of the symmetric group Sn. Let a_t (n)denote the number oft-core partitions of n. There are many interesting congruences proved by Granville, Ono, Garvan for the p-core partition functions a_p (n)where p is a prime. In this paper, we derive new congruences modulo 3 for the 11-core partition function a11(n) by using an identity given by Chan and Toh and a p-dissection of Ramanujan's theta functionf1 due to Cui and Gu.
Keywords: Congruences, Dissection, t-core partitions, Theta function.