6 citations · 13 across the 7 of their papers we have counts for
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Equivalence between Erdős-Hajnal and polynomial Rödl and Nikiforov conjectures
Matija Bucić, Jacob Fox, Huy Tuan Pham
It is well-known that polynomial versions of theorems of Rödl and Nikiforov, as conjectured by Fox and Sudakov and Nguyen, Scott and Seymour imply the classical Erdős-Hajnal conjec…
Small subsets with large sumset: Beyond the Cauchy--Davenport bound
Jacob Fox, Sammy Luo, Huy Tuan Pham +1
For a subset of an abelian group , given its size , its doubling , and a parameter which is small compared to , we study the size of the largest s…
Subset sums, completeness and colorings
David Conlon, Jacob Fox, Huy Tuan Pham
We develop novel techniques which allow us to prove a diverse range of results relating to subset sums and complete sequences of positive integers, including solutions to several l…
Tower-type bounds for Roth's theorem with popular differences
Jacob Fox, Huy Tuan Pham, Yufei Zhao
Green developed an arithmetic regularity lemma to prove a strengthening of Roth's theorem on arithmetic progressions in dense sets. It states that for every there is some $N…
Common and Sidorenko Linear Equations
Jacob Fox, Huy Tuan Pham, Yufei Zhao
A linear equation with coefficients in is common if the number of monochromatic solutions in any two-coloring of is asymptotically (as $n \to \infty…
Popular progression differences in vector spaces
Jacob Fox, Huy Tuan Pham
Green proved an arithmetic analogue of Szemerédi's celebrated regularity lemma and used it to verify a conjecture of Bergelson, Host, and Kra which sharpens Roth's theorem on three…