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math.CO2026
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…
math.CO2026
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…
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…