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Abstract for  William F. Doran IV,  A Plethysm Formula
for $p_\mu(\underline{x}) \circ h_\lambda(\underline{x})$

This paper gives a new formula for the plethysm of power-sum symmetric
functions and complete symmetric functions.  The form of the main result
is that for $\mu \vdash b$ and $\lambda \vdash a$ with length $t$, then 
  $$p_\mu(\underline{x}) \circ h_\lambda(\underline{x}) = \sum_T \underline{\omega}^{{\rm maj}_{\mu^t} (T)}
      s_{{\rm sh}(T)}(\underline{x}) $$
where the sum is over semistandard tableaux of weight $\lambda_1^b
\lambda_2^b \dots \lambda_t^b$ and $\underline{\omega}^{{\rm maj}_{\mu^t} (T)}$ is a root 
of unity which depends on $\mu$, $t$, and $T$.


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