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{\bf Pavlo Pylyavskyy}
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{\bf On Plethysm Conjectures of Stanley and Foulkes: The $2 \times n$ Case}
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We prove Stanley's plethysm conjecture for the $2 \times n$ case,
which composed with the work of Black and List provides another proof
of Foulkes conjecture for the $2 \times n$ case. We also show that the
way Stanley formulated his conjecture, it is false in general, and
suggest an alternative formulation.
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