AI 中文总结
该研究针对d≥2的情况构造了无穷多类对称抽象d-刚性拟阵，其中d=2时的拟阵为病态拟阵，还为Tyomkyn的猜想提供了反例。
AI 中文摘要
我们证明，对每个d≥2，存在无穷多个对称抽象d-刚性拟阵，它们既不是d-刚性拟阵、也不是d-超连通拟阵或d-余因子拟阵。当d=2时，我们构造的拟阵是病态的，即它们不包含在任何抽象2-刚性拟阵族中。该构造还为Tyomkyn的一个猜想提供了反例。
英文摘要
We prove that for each $d \geq 2$, there exist infinitely many symmetric abstract $d$-rigidity matroids that are not the $d$-rigidity matroid, the $d$-hyperconnectivity matroid, or the $d$-cofactor matroid. When $d=2$, our constructed matroids are pathological, in the sense that they are not contained within any abstract 2-rigidity matroid family. Our construction additionally provides a counter-example to a conjecture of Tyomkyn.
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