Vector representable matroids of given rank with given automorphism group |
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Authors: | László Babai |
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Institution: | Dept. of Algebra and Number Theory, Eötvös L. University, H-1088 Budapest, Hungary |
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Abstract: | A simple way of associating a matroid of prescribed rank with a graph is shown. The matroids so constructed are representable over any sufficiency large field. Their use is demonstrated by the following result: Given an integer k?3 and a function G associating a group with each subset of a set S, there is a matroid M(E), representable over any sufficiently large field, such that E ? S, and for any T ?/ S, the rank of M/Tis k, and the automorphine group of MT is isomorphic to G(T). |
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