• Corpus ID: 233289540

Combinatorial Bounds in Distal Structures

  title={Combinatorial Bounds in Distal Structures},
  author={Aaron Anderson},
We provide polynomial upper bounds for the minimal sizes of distal cell decompositions in several kinds of distal structures, particularly weakly o-minimal and P -minimal structures. The bound in general weakly o-minimal structures generalizes the vertical cell decomposition for semialgebraic sets, and the bounds for vector spaces in both o-minimal and p-adic cases are tight. We apply these bounds to Zarankiewicz’s problem and sum-product bounds in distal structures. 
1 Citations

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