Multilevel polynomial partitioning and semialgebraic hypergraphs:
regularity, Tur\'an, and Zarankiewicz results
Multilevel polynomial partitioning and semialgebraic hypergraphs:
regularity, Tur\'an, and Zarankiewicz results
We prove three results about semialgebraic hypergraphs. First, we prove an optimal and oblivious regularity lemma. Fox-Pach-Suk proved that the class of $k$-uniform semialgebraic hypergraphs satisfies a very strong regularity lemma where the vertex set can be partitioned into $\mathrm{poly}(1/\varepsilon)$ pieces so that all but an $\varepsilon$-fraction of $k$-tuples of …