1 citations · 1 across the 12 of their papers we have counts for
10 papers · 1 filter
Nonlinear lower-tail large deviations at criticality
Matthew Kwan, Huy Tuan Pham
We introduce general methods to derive lower tail large deviation principles, for a variety of nonlinear problems of combinatorial interest. These methods are especially effective…
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…
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…
Spread blow-up lemma with an application to perturbed random graphs
Rajko Nenadov, Huy Tuan Pham
Combining ideas of Pham, Sah, Sawhney, and Simkin on spread perfect matchings in super-regular bipartite graphs with an algorithmic blow-up lemma, we prove a spread version of the…
Short proof of the hypergraph container theorem
Rajko Nenadov, Huy Tuan Pham
We present a short and simple proof of the celebrated hypergraph container theorem of Balogh--Morris--Samotij and Saxton--Thomason. On a high level, our argument utilises the idea…
The largest subgraph without a forbidden induced subgraph
Jacob Fox, Rajko Nenadov, Huy Tuan Pham
We initiate the systematic study of the following Turán-type question. Suppose is a graph with vertices such that the edge density between any pair of subsets of vertices o…
The upper logarithmic density of monochromatic subset sums
David Conlon, Jacob Fox, Huy Tuan Pham
We show that in any two-coloring of the positive integers there is a color for which the set of positive integers that can be represented as a sum of distinct elements with this co…