Weak Maps and Stabilizers of Classes of Matroids
نویسندگان
چکیده
Let F be a field and let N be a matroid in a class N of F-representable matroids that is closed under minors and the taking of duals. Then N is an F-stabilizer for N if every representation of a 3-connected member of N is determined up to elementary row operations and column scaling by a representation of any one of its N-minors. The study of stabilizers was initiated by Whittle. This paper extends that study by examining certain types of stabilizers and considering the connection with weak maps. The notion of a universal stabilizer is introduced to identify the underlying matroid structure that guarantees that N will be an F9-stabilizer for N for every field F9 over which members of N are representable. It is shown that, just as with F-stabilizers, one can establish whether or not N is a universal stabilizer for N by an elementary finite check. If N is a universal stabilizer for N, we determine additional conditions on N and N that ensure that if N is not a strict rank-preserv-
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