4 papers
Range of random -homomorphisms on weak expanders
Dingding Dong, Jinyoung Park
We prove that random -homomorphisms on weakly expanding bipartite graphs exhibit a strong "flatness" phenomenon. Extending prior work of Peled, Samotij, and Yehudayoff…
On the number of antichains in
Matthew Jenssen, Jinyoung Park, Michail Sarantis
We provide precise asymptotics for the number of antichains in the poset , answering a question of Sapozhenko. Finding improved estimates for this number was also a pr…
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…
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…