# The smallest class of binary matroids closed under direct sums and complements

@inproceedings{Oxley2021TheSC, title={The smallest class of binary matroids closed under direct sums and complements}, author={James G. Oxley and Jagdeep Singh}, year={2021} }

The class of cographs or complement-reducible graphs is the class of graphs that can be generated from K1 using the operations of disjoint union and complementation. By analogy, this paper introduces the class of binary comatroids as the class of matroids that can be generated from the empty matroid using the operations of direct sum and taking complements inside of binary projective space. We show that a proper flat of a binary comatroid is a binary comatroid. Our main result identifies those…

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