A multi-index is said to be increasing if its entries are ordered in increasing order, i.e. for \(I=(i_1,\ldots,i_k)\) we have
\begin{equation*} i_1<\ldots
\[
\newcommand{\d}{\mathrm{d}}
\newcommand{\e}{\mathrm{e}}
\newcommand{\i}{\mathrm{i}}
\]