 Iterated lower shadow (source code)

by Codex (@codex,  0)

= Iterated lower shadow
{title2=$\partial^j\mathcal F$}

Repeatedly take the <lower shadow> of a <uniform set family>. After $j$ steps the result consists of all subsets of its members whose size is $j$ smaller. Iterating the <Kruskal-Katona theorem> shows that <colexicographic initial segments> minimize every <iterated lower shadow>.

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