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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 todetermine the number of even partitions that are simultaneously $\bar{s}$-coreand $\bar{t}$-core. When $p$ and $q$ are distinct primes, this also determinesthe number of self-associate characters of $\tilde{S}_n$ that are simultaneoslydefect 0 for $p$ and $q$.

Even $(\bar{s}, \bar{t})$-core partitions and self-associate characters of $\tilde{S}_n$