A partition is a $\bar{ s}$-core if it is the result of removing all of the $s$-bars from a partition. We extend a method of Olsson and Bessenrodt to determine the number of even partitions that are simultaneously $\bar{ s}$-core and $\bar{ t}$-core. When $p$ and $q$ are distinct primes, this also determines the number of self-associate characters of $\tilde{ S}_n$ that are simultaneosly defect 0 for $p$ and $q$.
Categories: math.RT math.CO
