Relaxations of GF$(4)$-representable matroids

Ben Clark; James Oxley; Stefan H. M. van Zwam

Relaxations of GF$(4)$-representable matroids

Combinatorics 2018-06-04 v3

Authors: Ben Clark , James Oxley , Stefan H. M. van Zwam

Abstract

We consider the GF $(4)$ -representable matroids with a circuit-hyperplane such that the matroid obtained by relaxing the circuit-hyperplane is also GF $(4)$ -representable. We characterize the structure of these matroids as an application of structure theorems for the classes of $U_{2,4}$ -fragile and $\{U_{2,5},U_{3,5}\}$ -fragile matroids. In addition, we characterize the forbidden submatrices in GF $(4)$ -representations of these matroids.

Keywords

matroid theory representation theory of groups

Cite

@article{arxiv.1704.07306,
  title  = {Relaxations of GF$(4)$-representable matroids},
  author = {Ben Clark and James Oxley and Stefan H. M. van Zwam},
  journal= {arXiv preprint arXiv:1704.07306},
  year   = {2018}
}

Comments

Jupyter notebook with SageMath code in ancillary files

Relaxations of GF$(4)$-representable matroids

Abstract

Keywords

Cite

Comments

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