Necessary conditions for the positivity of Littlewood-Richardson and plethystic coefficients

Abstract

We give necessary conditions for the positivity of Littlewood-Richardson coefficients and SXP coefficients. We deduce necessary conditions for the positivity of the plethystic coefficients. Explicitly, our main result states that if $S^{\lambda }(V)$ appears as a summand in the decomposition into irreducibles of $S^{\mu }(S^{\nu }(V))$, then $\nu$'s diagram is contained in $\lambda$'s diagram.

11 pages, 7 figures

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