Blasiak verified a conjecture of White for graphic matroids by showing that the toric ideal of a graphic matroid is generated by quadrics. In this paper, we extend this result to frame matroids satisfying a linearity condition. Such classes of matroids include graphic matroids, bicircular matroids, signed graphic matroids, and more generally frame matroids obtained from group-labelled graphs.

中文翻译：

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框架拟阵、复曲面理想和怀特猜想

Blasiak 通过证明图形拟阵的复曲面理想是由二次曲线生成的，验证了 White 对图形拟阵的猜想。在本文中，我们将此结果扩展到满足线性条件的框架拟阵。此类拟阵包括图形拟阵、双圆拟阵、带符号图形拟阵，以及更一般的从组标记图中获得的框架拟阵。