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Some remarks on Ramsey matroids. (English) Zbl 0543.05021

Results on Ramsey matroids together with some open problems are summarized. Using the method of matroid amalgamation, the following theorem is proved. Let M be a matroid and G be a subgroup of its automorphism group Aut M. Then there exists a matroid N such that (i) M is a restriction of N, (ii) Aut N is isomorphic to G, (iii) every automorphism of G extends uniquely to an automorphism of N.

MSC:

05B35 Combinatorial aspects of matroids and geometric lattices
20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures
05C55 Generalized Ramsey theory
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