8 citations · 11 across the 15 of their papers we have counts for
15 papers
On the Diameter of Finite Sidon Sets
Daniel Carter, Zach Hunter, Kevin O'Bryant
We prove that the diameter of a Sidon set (also known as a Babcock sequence, Golomb ruler, or set) with elements is at least where , a…
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…
Induced -free subgraphs with large average degree
Xiying Du, António Girão, Zach Hunter +2
We prove that there exists a constant so that, for all , if has average degree at least and does not contain as a subgraph then it…
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…
Lower bounds for multicolor van der Waerden numbers
Zach Hunter
We give an exponential improvement to the diagonal van der Waerden numbers for colors.
A new upper bound to (a variant of) the pancake problem
Zach Hunter
The "pancake problem" asks how many prefix reversals are sufficient to sort any permutation to the identity. We write to denote this quantity. The best…
Corner-free sets via the torus
Zach Hunter
A corner is a triple of points in of the form where . One can think of them as being 2D-analogues to 3-term arithmetic progressions. In…
A short proof that
Zach Hunter
Here we present a short proof that the two-color van der Waerden number is bounded from below by . Previous work has already shown that a superpolynomial lowe…
A note on large induced subgraphs with prescribed residues in bipartite graphs
Zach Hunter
It was proved by Scott that for every , there exists a constant such that for every bipartite -vertex graph without isolated vertices, there exists an induce…
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…
Improved lower bounds for van der Waerden numbers
Zach Hunter
Recently, Ben Green proved that the two-color van der Waerden number is bounded from below by where $b_0(k) = c_0\left(\frac{\log k }{\log \log k}\right)^{1/3…
An asymptotically tight lower bound for superpatterns with small alphabets
Zach Hunter
A permutation is a -superpattern (or -universal) if it contains each as a pattern. This notion of "superpatterns" can be generalized to words on smaller…
Multi-Scale Merge-Split Markov Chain Monte Carlo for Redistricting
Eric A. Autry, Daniel Carter, Gregory Herschlag +2
We develop a Multi-Scale Merge-Split Markov chain on redistricting plans. The chain is designed to be usable as the proposal in a Markov Chain Monte Carlo (MCMC) algorithm. Samplin…
Metropolized Forest Recombination for Monte Carlo Sampling of Graph Partitions
Eric Autrey, Daniel Carter, Gregory Herschlag +2
We develop a new Markov chain on graph partitions that makes relatively global moves yet is computationally feasible to be used as the proposal in the Metropolis-Hastings method. O…
Optimal Legislative County Clustering in North Carolina
Daniel Carter, Zach Hunter, Dan Teague +2
North Carolina's constitution requires that state legislative districts should not split counties. However, counties must be split to comply with the "one person, one vote" mandate…