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arXiv · 1309.5329

Matroids with a modular 4-point line

Rohan Kapadia
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Abstract

A result of Seymour implies that any 3-connected matroid with a modular 3-point line is binary. We prove a similar characterization for 3-connected matroids with modular 4-point lines. We show that such a matroid is either representable over GF(3) or GF(4) or has an $F_7$-minor and either an $(F_7^-)$- or $(F_7^-)^*$-minor.

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Rohan Kapadia. 2014-03-24. Matroids with a modular 4-point line. https://doi.org/10.1137/130937937

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