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arxiv: 1704.07306 · v3 · pith:V6CGZIHFnew · submitted 2017-04-24 · 🧮 math.CO

Relaxations of GF(4)-representable matroids

classification 🧮 math.CO
keywords matroidsrepresentablecharacterizecircuit-hyperplanefragilestructureadditionapplication
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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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