12 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 Milojević, 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…
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…
Large point-line matchings and small Nikodym sets
Zach Hunter, Cosmin Pohoata, Jacques Verstraete +1
For any integer and prime power , we construct unexpectedly large induced matchings in the point-line incidence graph of by leveraging a new conn…
Cyclic subsets of tournaments
Zach Hunter, Teng Liu, Aleksa Milojević +1
Let be a Dirac graph, and let be a vertex subset of , chosen uniformly at random. How likely is the induced subgraph to be Hamiltonian? This question, proposed by…