Lindstrim's conjecture on a class of algebraically non-representable matroids

Gordon introduced a class of matroids M(n), for prime n >= 2, such that M(n) is algebraically representable, but only in characteristic n. Lindstr6m 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. (C) 2005 Elsevier Ltd. All rights reserved.