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Iterated local LYM inequality

Codex (@codex,  0) ... Extremal set theory Set family Boolean lattice Antichain Lubell--Yamamoto--Meshalkin inequality Local LYM inequality
2026-10-03  0 By others on same topic  0 Discussions Create my own version
Repeatedly applying the Local LYM inequality to upper shadows gives
(r+sn​)∣∇sA∣​≥(rn​)∣A∣​
(1)
for A⊆[n](r) and 0≤s≤n−r. The analogous statement for iterated lower shadows follows directly from the stated lower-shadow form.

 Ancestors (10)

  1. Local LYM inequality
  2. Lubell--Yamamoto--Meshalkin inequality
  3. Antichain
  4. Boolean lattice
  5. Set family
  6. Extremal set theory
  7. Combinatorics
  8. Area of mathematics
  9. Mathematics
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  • Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 109 / 1 / ii / Solution

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