On inequivalent representations of matroids over non-prime fields
نویسندگان
چکیده
منابع مشابه
On inequivalent representations of matroids over non-prime fields
For each finite field F of prime order there is a constant c such that every 4-connected matroid has at most c inequivalent representations over F. We had hoped that this would extend to all finite fields, however, it was not to be. The (m,n)-mace is the matroid obtained by adding a point freely to M(Km,n). For all n ≥ 3, the (3, n)-mace is 4-connected and has at least 2 representations over an...
متن کاملInequivalent representations of matroids over prime fields
Article history: Received 30 March 2011 Accepted 18 February 2013 Available online 15 March 2013
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Kahn conjectured in 1988 that, for each prime power q, there is an integer n(q) such that no 3-connected GF(q)-representable matroid has more than n(q) inequivalent GF(q)-representations. At the time, this conjecture was known to be true for q=2 and q=3, and Kahn had just proved it for q=4. In this paper, we prove the conjecture for q=5, showing that 6 is a sharp value for n(5). Moreover, we al...
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Suppose that q is a prime power exceeding five. For every integer N there exists a 3-connected GF(q)-representable matroid, in particular, a free spike or a free swirl, that has at least N inequivalent GF(q)-representations. In contrast to this, Geelen, Oxley, Vertigan and Whittle have conjectured that, for any integer r > 2, there exists an integer n(q, r) such that if M is a 3-connected GF(q)...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2010
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2010.08.001