4 papers
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…
A new lower bound for the Ramsey numbers
Marcelo Campos, Matthew Jenssen, Marcus Michelen +1
We prove a new lower bound for the off-diagonal Ramsey numbers, \[ R(3,k) \geq \bigg( \frac{1}{3}+ o(1) \bigg) \frac{k^2}{\log k }\, , \] thereby narrowing the gap between the uppe…
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…