17 citations · 37 across the 17 of their papers we have counts for
7 papers · 1 filter
Gilbreath's conjecture: a Cramér random model and a deterministic analysis
Zachary Chase, Zach Hunter, Terence Tao
Gilbreath's conjecture asserts that if one starts with the sequence of primes and takes successive absolute differences to create a triangular array, then the left diagonal of this…
Approximate union closed conjecture
Zachary Chase, Shachar Lovett
A set system is called union closed if for any two sets in the set system their union is also in the set system. Gilmer recently proved that in any union closed set system some ele…
On the smallest gap in a sequence with Poisson pair correlations
Daniel Altman, Zachary Chase
We prove that any increasing sequence of real numbers with average gap and Poisson pair correlations has some gap that is at least . This improves upon a result of…
A new upper bound for separating words
Zachary Chase
We prove that for any distinct , there is a deterministic finite automaton with states that accepts but not . This improves Robso…
A random analogue of Gilbreath's conjecture
Zachary Chase
A well-known conjecture of Gilbreath, and independently Proth from the 1800s, states that if denotes the prime number and $a_{i,n} = |a_{i-1,n}-a_{i…
The Maximum Number of Triangles in a Graph of Given Maximum Degree
Zachary Chase
We prove that any graph on vertices with max degree has at most triangles, where , . This resolves a conjectur…
The Maximum Number of Three Term Arithmetic Progressions, and Triangles in Cayley Graphs
Zachary Chase
Let be a finite Abelian group. For a subset , let denote the number of length three arithemtic progressions in and Prob[] $= \frac{1}{|S|^2}\sum_…