 Solution

ID: past-exam-of-the-computer-science-course-of-the-university-of-oxford/2023/combinatorial-optimisation/2/c/vii/solution

By (ii),

Y \subseteq σ (Y)

, and by (vi) these subsets have equal rank of a matroid. Apply (v) to this pair to obtain

σ (σ (Y)) = σ (Y) .

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