Topology

Coatoms of the lattice of funcoids ★

Author(s): Porton

Problem   Let $ A $ and $ B $ be infinite sets. Characterize the set of all coatoms of the lattice $ \mathsf{FCD}(A;B) $ of funcoids from $ A $ to $ B $. Particularly, is this set empty? Is $ \mathsf{FCD}(A;B) $ a coatomic lattice? coatomistic lattice?

Keywords: atoms; coatoms; funcoids

Posted by porton
updated April 24th, 2014
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Combinatorics » Posets

Saturated $k$-Sperner Systems of Minimum Size ★★

Author(s): Morrison; Noel; Scott

Question   Does there exist a constant $ c>1/2 $ and a function $ n_0(k) $ such that if $ |X|\geq n_0(k) $, then every saturated $ k $-Sperner system $ \mathcal{F}\subseteq \mathcal{P}(X) $ has cardinality at least $ 2^{(1+o(1))ck} $?

Keywords: antichain; extremal combinatorics; minimum saturation; saturation; Sperner system

Posted by Jon Noel
updated April 12th, 2014
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