An extermal problem in finite geometry
|Affiliation:||University of Waterloo|
|Room:||Mathematics & Computer Building (MC) 5158|
For a given restriction $H$ of PG$(m-1,q)$ and any $n>m$, we consider the maximum number of points in PG$(n-1,q)$ not containing a copy of $H$. We prove a striking analogue of the Erdös-Stone Theorem. The proof is surprisingly easy, but relies on a very deep result related to the density version of the multidimensional Hales-Jewett theorem.
This is joint work with Peter Nelson.
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