A Density Hales-Jewett Theorem for matroids

2012/10/16 by Jim Geelen, Peter Nelson, Geelen, Jim +1 · 1 citation
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.1210.4522

openalex publication_date 2012/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that, if α> 0 is a real number, n ≥ 2 and ℓ ≥ 2 are integers, and q is a prime power, then every simple matroid M of sufficiently large rank, with no U_2,ℓ-minor, no rank-n projective geometry minor over a larger field than \GF(q), and satisfying |M| ≥ αq^r(M), has a rank-n affine geometry restriction over \GF(q). This result can be viewed as an analogue of the Multidimensional Density Hales-Jewett Theorem for matroids.

Citations

• A new proof of the density Hales-Jewett theorem

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