18 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…
Nearly tight bounds for induced subdivisions
Zach Hunter, Aleksa MilojeviÄ, Patryk Morawski +1
Subdivisions of complete graphs play a central role in combinatorics, having deep connections to structural, extremal, and topological aspects of graph theory. A celebrated conject…
Three-color van der Waerden numbers grow super-exponentially
Jacob Fox, Zach Hunter
For sufficiently large, we show that there is a three-coloring of the first positive integers without any monochromatic -term arithmetic progressions. T…
Gaussian random graphs and Ramsey numbers
Zach Hunter, Aleksa MilojeviÄ, Benny Sudakov
We give a simple proof of the recent remarkable exponential improvement for Ramsey lower bounds, obtained by Ma, Shen and Xie. Our key ingredient is an alternative construction bas…
Permanents of random matrices over finite fields
Zach Hunter, Matthew Kwan, Lisa Sauermann
Fix a finite field and let be a uniformly random matrix over . The asymptotic distribution of the determinant…
Induced subdivisions of in graphs of high girth
António Girão, Zach Hunter
In this paper, we show that for all , every graph with minimum degree and girth at least contains an induced subdivision of a . This answers a probl…