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math.CO2024
On Dedekind's problem, a sparse version of Sperner's theorem, and antichains of a given size in the Boolean lattice
Matthew Jenssen, Alexandru Malekshahian, Jinyoung Park
Dedekind's problem, dating back to 1897, asks for the total number of antichains contained in the Boolean lattice on elements. We study Dedekind's problem using a…
math.CO2024
A refined graph container lemma and applications to the hard-core model on bipartite expanders
Matthew Jenssen, Alexandru Malekshahian, Jinyoung Park
We establish a refined version of a graph container lemma due to Galvin and discuss several applications related to the hard-core model on bipartite expander graphs. Given a graph…
math.CO2024
On a clique-building game of Erdős
Alexandru Malekshahian, Sam Spiro
The following game was introduced in a list of open problems from 1983 attributed to Erdős: two players take turns claiming edges of a until all edges are exhausted. Player 1…