Lower shadow
= Lower shadow
{title2=$\partial\mathcal A$}
{wiki}
The lower shadow of $\mathcal A\subseteq[n]^{(r)}$ is
$$
\partial\mathcal A=\{B\in[n]^{(r-1)}:B\subset A\text{ for some }A\in\mathcal A\}.
$$
= Lower shadow
{title2=$\partial\mathcal A$}
{wiki}
The lower shadow of $\mathcal A\subseteq[n]^{(r)}$ is
$$
\partial\mathcal A=\{B\in[n]^{(r-1)}:B\subset A\text{ for some }A\in\mathcal A\}.
$$