  Let $p$ be an odd prime. The bar partitions with sign and $p$-bar-core
partitions with sign respectively label the spin characters and $p$-defect zero
spin characters of the double cover of the symmetric group, and by restriction,
those of the alternating group. The generating functions for these objects have
been determined by J. Olsson. We study these functions from an arithmetic
perspective, using classical analytic tools and elementary generating function
manipulation to obtain many Ramanujan-like congruences.
