Elementary set shift
= Elementary set shift
{title2=$S_{ij}$}
For $i<j$, replace a member $A$ containing $j$ but not $i$ by $(A\setminus\{j\})\cup\{i\}$ only when the replacement is absent. An <elementary set shift> preserves family size and the <intersecting family> property. The inclusion $\partial(S_{ij}\mathcal F)\subseteq S_{ij}(\partial\mathcal F)$ shows that it cannot increase the <lower shadow>.