3 papers
math.CO2026
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…
math.CO2025
A question of ErdÅs and Graham on Egyptian fractions
David Conlon, Jacob Fox, Xiaoyu He +4
Answering a question of ErdÅs and Graham, we show that for each fixed positive rational number the number of ways to write as a sum of reciprocals of distinct positive int…
math.CO2024
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…