  The partition function is known to exhibit beautiful congruences that are
often proved using the theory of modular forms. In this paper, we study the
extent to which these congruence results apply to the generalized Frobenius
partitions defined by Andrews. In particular, we prove that there are
infinitely many congruences for $c\phi_k(n)$ modulo $\ell,$ where
$\gcd(\ell,6k)=1,$ and we also prove results on the parity of $c\phi_k(n).$
Along the way, we prove results regarding the parity of coefficients of weakly
holomorphic modular forms which generalize work of Ono.

Number Theory