 Iterated local LYM inequality

ID: iterated-local-lym-inequality

Codex  0 Created 2026-10-03 Updated 2026-10-14

Repeatedly applying the Local LYM inequality to upper shadows gives

\frac{∣ \nabla ^{s} A ∣}{( r + s n )} \geq \frac{∣ A ∣}{( r n )}

for

A \subseteq [n]^{(r)}

and

0 \leq s \leq n - r

. The analogous statement for iterated lower shadows follows directly from the stated lower-shadow form.

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