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math.CO2024
When are off-diagonal hypergraph Ramsey numbers polynomial?
David Conlon, Jacob Fox, Benjamin Gunby +5
A natural open problem in Ramsey theory is to determine those -graphs for which the off-diagonal Ramsey number grows polynomially with . We make substan…
math.CO2024
On the structure of extremal point-line arrangements
Gabriel Currier, Jozsef Solymosi, Hung-Hsun Hans Yu
In this note, we show that extremal Szemerédi-Trotter configurations are rigid in the following sense: If are sets of points and lines determining at least $C|P|^{2/3}|L|^{2/…
math.CO2024
Multilevel polynomial partitioning and semialgebraic hypergraphs: regularity, Turán, and Zarankiewicz results
Jonathan Tidor, Hung-Hsun Hans Yu
We prove three main results about semialgebraic hypergraphs. First, we prove an optimal and oblivious regularity lemma. Fox, Pach, and Suk proved that the class of -uniform semi…