= Generating series of the Kostant partition function
{title2=$\sum_\nu p(\nu)e^{-\nu}=\prod_{\alpha>0}(1-e^{-\alpha})^{-1}$}
The <Kostant partition function> counts <nonnegative integer> combinations of the positive <roots of a root system>, without ordering the summands. Multiply the formal <geometric series> $\sum_{k\geq0}e^{-k\alpha}$ for every <positive root>. The coefficient of $e^{-\nu}$ counts precisely these combinations. Every coefficient is finite because a <linear functional> strictly positive on the <positive roots> bounds every participating integer coefficient. The sign of each exponent in the cancelling product must agree with that of this series.
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