Matroids representable over fields with a common subfield

2014/01/27 by Peter Nelson, Nelson, Peter, Stefan H. M. van Zwam +1
Mathematics · #05B35 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05B35

paper · pdf · doi:10.48550/arxiv.1401.7040

21 pages

arxiv created 2014/01/27 · arxiv updated 2014/01/29

Abstract

A matroid is GF(q)-regular if it is representable over all proper superfields of the field GF(q). We show that, for highly connected matroids having a large projective geometry over GF(q) as a minor, the property of GF(q)-regularity is equivalent to representability over both GF(q²) and GF(q^t) for some odd integer t ≥ 3. We do this by means of an exact structural description of all such matroids.

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