Abstract:A matroid M is an ordered pair (E, I), where E is a finite set called the ground set and a collection I ⊂ 2 E called the independent sets which satisfy the conditions: (I1) ∅ ∈ I, (I2) I ⊂ I ∈ I implies I ∈ I, and (I3) I1, I2 ∈ I and |I1| < |I2| implies that there is an e ∈ I2 such that I1 ∪ {e} ∈ I. The rank rk(M ) of a matroid M is the maximum size of an independent set. We say that a matroid M = (E, I) is representable over the reals if there is a map ϕ : E → R rk(M ) such that I ∈ I if and only if ϕ(I) for… Show more
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