Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  prove that a binary matroid with huge branch-width contains the cycle matroid of a large grid as a minor. This implies that an infinite antichain of binary matroids cannot contain the cycle matroid of a planar graph. The result also holds for any other finite field.
['Jim Geelen', 'Bert Gerards', 'Geoff Whittle']
I am writing a research paper on a idea Excluding a planar graph from GF(q)-representable matroids
[{"from": "human", "value": "I am writing a research paper on a idea Excluding a planar graph from GF(q)-representable matroids"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  prove that a binary matroid with huge branch-width contains the cycle matroid of a large grid as a minor. This implies that an infinite antichain of binary matroids cannot contain the cycle matroid of a planar graph. The result also holds for any other finite field."}]