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We prove that if a matroid M contains two disjoint bases (or, dually, if its ground set is the union of two bases), then T M (a, a) ≤ max{T M (2a, 0), T M (0, 2a)} for a ≥ 2. This resembles the conjecture that appears in C. Merino and D. (0, 2)} for matroids which contains two disjoint bases or its ground set is the union of two bases. We also prove the… (More)

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