Research Papers

aequationes mathematicae

, Volume 4, Issue 1, pp 44-50

First online:

Matroids with sylvester property

  • U. S. R. MurtyAffiliated withUniversity of Waterloo

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Let 〈M, ℐ〉 be a matroid of rankn, n being a non-negative integer. Let the matroid have the property that any two distinct cells ofM are contained in a circuit of size 3. Then we prove that |M| ⩾ 2 n −1. We also establish that, up to isomorphism, the matroid corresponding to the non-nulln-tuples of the elements of GF(2) is the unique extremal matroid.