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An analogue of the Erdős-Stone theorem for finite geometries

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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-(m−c) 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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Authors and Affiliations

  1. Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Canada

    Jim Geelen

  2. School of Mathematics Statistics and Operations Research, Victoria University, Wellington, New Zealand

    Peter Nelson

Authors
  1. Jim Geelen
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  2. Peter Nelson
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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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  • DOI: https://doi.org/10.1007/s00493-014-2952-3

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