17 citations · 37 across the 17 of their papers we have counts for
18 papers
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…
Replicability and stability in learning
Zachary Chase, Shay Moran, Amir Yehudayoff
Replicability is essential in science as it allows us to validate and verify research findings. Impagliazzo, Lei, Pitassi and Sorrell (`22) recently initiated the study of replicab…
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 length of Pierce expansions
Zachary Chase, Mayank Pandey
For a given positive integer , how long can the process last before reaching ? We improve Erdős and Shallit's upper bound of $O(n^{\frac{…
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…
Optimally compressing VC classes
Zachary Chase
Resolving a conjecture of Littlestone and Warmuth, we show that any concept class of VC-dimension has a sample compression scheme of size .
On sumsets containing a perfect square
Zachary Chase
We show contains a perfect square if have . The constant is optimal.
Approximate trace reconstruction of random strings from a constant number of traces
Zachary Chase, Yuval Peres
In the trace reconstruction problem, the goal is to reconstruct an unknown string of length from multiple traces obtained by passing through the deletion channel. In th…
Collision Recovery Control of a Foldable Quadrotor
Karishma Patnaik, Shatadal Mishra, Zachary Chase +1
Autonomous missions of small unmanned aerial vehicles (UAVs) are prone to collisions owing to environmental disturbances and localization errors. Consequently, a UAV that can endur…
New upper bounds for trace reconstruction
Zachary Chase
We show that any -bit string can be recovered with high probability from independent random subsequences.
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…
Experimental Evidence for Asymptotic Non-Optimality of Comb Adversary Strategy
Zachary Chase
For the problem of prediction with expert advice in the adversarial setting with finite stopping time, we give strong computer evidence that the comb strategy for experts is…
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…
Additive Conjugacy and the Bohr Compactification of Orthogonal Representations
Zachary Chase, Wade Hann-Caruthers, Omer Tamuz
We say that two unitary or orthogonal representations of a finitely generated group are additive conjugates if they are intertwined by an additive map, which need not be contin…
New Lower Bounds for Trace Reconstruction
Zachary Chase
We improve the lower bound on worst case trace reconstruction from to . As a consequence, we…
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_…
On the Iterates of Digit Maps
Zachary Chase
Given a base , a "digit map" is a map of the form , for each $…