Vector representable matroids of given rank with given automorphism group

✍ Scribed by László Babai

• Publisher: Elsevier Science
• Year: 1978
• Tongue: English
• Weight: 471 KB
• Volume: 24
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(78)90190-5

✦ Synopsis

A simple way of as,;ociating a matroid of prescribed rank with a graph is shown. The matroids so corhstrueted are re.presentable over any sufficiently large field. Their ase is demonstrated by the fallowing result: Given an integer k >~ 3 and a hmction G associating a group with each subsel of a set S, the'e is a matroid M(E), representable ever any sufl]ciendy large field, such that E ~S, and for rely TcS, the rank of MkT is k, and the automo~phi~m group of MkT is isomorphic to G(T).