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On plethysm conjectures of Stanley and Foulkes: the $2 \times n$ case

Pavlo Pylyavskyy
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Abstract

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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Pavlo Pylyavskyy. 2004-06-26. On plethysm conjectures of Stanley and Foulkes: the $2 \times n$ case. https://arxiv.org/abs/math/0406539

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