New Congruences Modulo 3 for 11-Core Partition Function
If t is a positive integer, then a partition of a nonnegativeintegern 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(n)denote the number of t-core partitions of n. There are many interesting
congruences proved by Granville, Ono, Garvan for the p-core partition functions a(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.