9 papers · 1 filter
No--in-line problem for
Anubhab Ghosal, Ritesh Goenka, Alexandr Grebennikov +3
What is the maximum number of points one can place in an grid such that every Euclidean line contains at most points? For , this is the notorious no-three-i…
A note on arithmetic progressions with restricted differences
David Conlon, Jacob Fox, Huy Tuan Pham
In this note, we show how to adapt Tao's slice rank method to extend the Ellenberg--Gijswijt theorem on cap sets to the problem of forbidding arithmetic progressions with restricte…
Random Cayley graphs and random sumsets
Noga Alon, Huy Tuan Pham
We prove that any finite abelian group contains a collection of not too many subsets with a special structure, so that for every subset of with a small doubling, there…
On the clique number of random Cayley graphs and related topics
David Conlon, Jacob Fox, Huy Tuan Pham +1
We prove that a random Cayley graph on a group of order has clique number with high probability. This bound is best possible up to the constant factor f…
A sharp version of Talagrand's selector process conjecture and an application to rounding fractional covers
Huy Tuan Pham
Expectation thresholds arise from a class of integer linear programs (LPs) that are fundamental to the study of thresholds in large random systems. An avenue towards estimating exp…
On monochromatic solutions to linear equations over the integers
Dingding Dong, Nitya Mani, Huy Tuan Pham +1
We study the number of monochromatic solutions to linear equations in a -coloring of . We show that any nontrivial linear equation has a constant fraction of sol…