\begin{abstract}
The problem of deciding containment of aggregate queries is
investigated. Containment is reduced to equivalence for queries with
{\em expandable\/} aggregation functions. Many common aggregation
functions, such as $\MAX$, $\CNTD$ (count distinct), $\COUNT$, $\SUM$,
$\AVG$, $\MDN$ 
 and $\STDV$ (standard deviation) are shown to be expandable. It is
shown that even in the 
presence of integrity constraints, containment can be reduced to
equivalence. For conjunctive \COUNT\ and \SUM-queries, simpler
characterizations for containment are given, that do not require
checking equivalence. These results are built upon in order to solve
the problem of finding maximally-contained sets of rewritings for
conjunctive \COUNT-queries. 
\end{abstract}

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