Matroid Representation , Geometry and Matrices
نویسنده
چکیده
The connections between algebra and finite geometry are very old, with theorems about configurations of points dating to ancient Greece. In these notes, we will put a matroid theoretic spin on these results, with matroid representations playing the central role. Recall the definition of a matroid via independent sets I. Definition 1.1. Let E be a finite set and let I be a family of subsets of E. Then the family I forms the independent sets of a matroid M if: (I1) I 6 = ∅ (I2) If J ∈ I and I ⊆ J , then I ∈ I (I3) If I, J ∈ I with |I| < |J |, then there is some element x ∈ J − I with I ∪ {x} ∈ I
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