Abstract
Gordon introduced a class of matroids M(n), for prime n≥2, such that M(n) is algebraically representable, but only in characteristic n. Lindström proved that M(n) for general n≥2 is not algebraically representable if n>2 is an even number, and he conjectured that if n is a composite number it is not algebraically representable. We introduce a new kind of matroid called a harmonic matroid of which the full algebraic matroid is an example. We prove the conjecture in this more general case.
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