The smallest class of binary matroids closed under direct sums and complements
Abstract
The class of cographs or complementreducible graphs is the class of graphs that can be generated from $K_1$ 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 binary noncomatroids for which every proper flat is a binary comatroid. The paper also proves the corresponding results for ternary matroids.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.09636
 Bibcode:
 2021arXiv211009636O
 Keywords:

 Mathematics  Combinatorics;
 05B35;
 05C25
 EPrint:
 26 pages, 10 figures