Dependencies among dependencies in matroids
In 1971, Rota introduced the concept of derived matroids to investigate “de-pendencies among dependencies” in matroids. In this paper, we study the derived matroid δM of an F-representation of a matroid M. The matroid δM has a naturally associated F-representation, so we can define a sequence δM, δ2M,. The main result classifies such derived sequences of matroids into three types: finite, cyclic, and divergent. For the first two types, we obtain complete characterizations and thereby resolve some of the questions that Longyear posed in 1980 for binary matroids. For the last type, the divergence is estimated by the coranks of the matroids in the derived sequence.
Publication Source (Journal or Book title)
Electronic Journal of Combinatorics
Oxley, J., & Wang, S. (2019). Dependencies among dependencies in matroids. Electronic Journal of Combinatorics, 26 (3) https://doi.org/10.37236/8742