Entropy, independent sets and antichains: A new approach to Dedekind's problem

By J. Kahn. 2001

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The Repulsive Lattice Gas, the Independent-Set Polynomial, and the Lovász Local Lemma (2003, background): “.4.2 Lower bounds on λc . . . . . . . . . . . . . . . . . . . . . . . . 88 2 1 Introduction The lattice gas with repulsive pair interactions is an important model in equilibrium statistical mechanics [36, 46, 59, 57, 60, 95, 6, 7, 12, 55, 26, 110, 61, 50, 102, 70, 71,43]. In the special case ofa har”
Ramsey Theory, integer partitions and a new proof of the Erdős–Szekeres Theorem (2012, background): “We note that by now there are several proofs [12, 14, 15, 22] of Kleitmen’s result10 but as of now we are not able to apply any of them in order to prove that the number of antichains in [n]d is of order 2O(n d−1/ √ d).”