The Toric Ideal of a Matroid of Rank 3 is Generated by Quadrics

The Toric Ideal of a Matroid of Rank 3 is Generated by Quadrics

White conjectured that the toric ideal associated with the basis of a matroid is generated by quadrics corresponding to symmetric exchanges. We present a combinatorial proof of White's conjecture for matroids of rank 3 by using a lemma proposed by Blasiak.

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Veröffentlicht in:The Electronic journal of combinatorics 2010-02, Vol.17 (1)
1. Verfasser: Kashiwabara, Kenji
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description White conjectured that the toric ideal associated with the basis of a matroid is generated by quadrics corresponding to symmetric exchanges. We present a combinatorial proof of White's conjecture for matroids of rank 3 by using a lemma proposed by Blasiak.
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title The Toric Ideal of a Matroid of Rank 3 is Generated by Quadrics
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