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Sperner system
Saturated $k$-Sperner Systems of Minimum Size ★★
Author(s): Morrison; Noel; Scott
Question Does there exist a constant
and a function
such that if
, then every saturated
-Sperner system
has cardinality at least
?
![$ c>1/2 $](/files/tex/71b371b57345af0cbcfd2ffd78362b8988723a7d.png)
![$ n_0(k) $](/files/tex/77717a7ba8441af96e47411a5b9a5d4a913f3dba.png)
![$ |X|\geq n_0(k) $](/files/tex/e6c6b51d4e2df6fd85840bc289e38c981674e057.png)
![$ k $](/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png)
![$ \mathcal{F}\subseteq \mathcal{P}(X) $](/files/tex/cb32025ab3209d1516fd6ea63a4d8eb206a81411.png)
![$ 2^{(1+o(1))ck} $](/files/tex/1564812bc34ed3ebd060debb561be85acfb45f10.png)
Keywords: antichain; extremal combinatorics; minimum saturation; saturation; Sperner system
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