4 papers
math.CO2023
On a method of Alweiss
Zach Hunter
Recently, Alweiss settled Hindman's conjecture over the rationals. In this paper, we provide our own exposition of Alweiss' result, and show how to modify his method to also show t…
math.CO2023
A notion of twins
Zach Hunter
Given a combinatorial structure, a ``twin'' is a pair of disjoint substructures which are isomorphic (or look the same in some sense). In recent years, there have been many problem…
math.CO2023
Lower bounds for multicolor van der Waerden numbers
Zach Hunter
We give an exponential improvement to the diagonal van der Waerden numbers for colors.
math.CO2021
Optimally reconstructing caterpillars
Zach Hunter
For a graph , the -deck of is the multiset of induced subgraphs on having vertices. Recently, Groenland et al. proved that any tree can be reconstructed fro…