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arXiv · 1704.07306

Relaxations of GF$(4)$-representable matroids

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

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Ben Clark, James Oxley, Stefan H. M. van Zwam. 2018-06-01. Relaxations of GF$(4)$-representable matroids. https://arxiv.org/abs/1704.07306

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