An analogue of the Erdős-Stone theorem for finite geometries

Abstract

For a set G of points in PG(m−1,q), let ex q (G;n) denote the maximum size of a collection of points in PG(n−1,q) not containing a copy of G, up to projective equivalence. We show that

where c is the smallest integer such that there is a rank-(mc) flat in PG(m−1,q) that is disjoint from G. The result is an elementary application of the density version of the Hales-Jewett Theorem.

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Correspondence to Jim Geelen.

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Geelen, J., Nelson, P. An analogue of the Erdős-Stone theorem for finite geometries. Combinatorica 35, 209–214 (2015). https://doi.org/10.1007/s00493-014-2952-3

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Mathematics Subject Classification (2010)

  • 05B35