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{\bf C. Klivans and V. Reiner}
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{\bf Shifted Set Families, Degree Sequences, and Plethysm}
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We study, in three parts, degree sequences of $k$-families
(or $k$-uniform hypergraphs) and shifted $k$-families.
%\begin{enumerate}
\item{$\bullet$}
The first part collects for the first time in one place, various implications
such as
$$ \scriptstyle
\hbox{Threshold} \Rightarrow \hbox{Uniquely Realizable}
\Rightarrow \hbox{Degree-Maximal} \Rightarrow \hbox{Shifted}
$$
which are equivalent concepts for $2$-families (= simple graphs), but
strict implications for $k$-families with $k \geq 3$. The
implication that uniquely realizable implies degree-maximal seems to be new.
\item{$\bullet$}
The second part recalls Merris and Roby's reformulation of the characterization
due to Ruch and Gutman for graphical degree sequences and shifted $2$-families.
It then introduces two generalizations which are characterizations
of shifted $k$-families.
\item{$\bullet$}
The third part recalls the connection between degree sequences of $k$-families
of size $m$ and the plethysm of elementary symmetric functions $e_m[e_k]$.
It then uses highest weight theory to explain how
shifted $k$-families provide the ``top part'' of these plethysm expansions,
along with offering a conjecture about a further relation.
%\end{enumerate}
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