移位拟阵与阈值拟阵
Shifted and Threshold Matroids
AI总结：
本文通过定义基的结构刻画阈值拟阵，构造非阈值的移位拟阵例子，给出阈值拟阵同构类计数公式，并设计多项式时间判定算法。
摘要：
我们通过定义基的结构刻画了阈值拟阵的类。我们还给出了一个移位拟阵但不是阈值拟阵的例子，回答了 Deza 和 Onn 的一个问题。最后，我们探讨了阈值拟阵刻画的结果：对于基集大小为 n 的阈值拟阵，我们给出了其同构类数目的公式。这一计数表明，几乎所有的移位拟阵都不是阈值拟阵。我们还提出了一个多项式时间算法来检查一个拟阵是否为阈值拟阵，并对 Deza 和 Onn 的一些主要结果给出了替代且简化的证明。
英文摘要：
We characterize the class of threshold matroids by the structure of their defining bases. We also give an example of a shifted matroid which is not threshold, answering a question of Deza and Onn. We conclude by exploring consequences of our characterization of threshold matroids: We give a formula for the number of isomorphism classes of threshold matroids on a ground set of size n. This enumeration shows that almost all shifted matroids are not threshold. We also present a polynomial-time algorithm to check if a matroid is threshold and provide alternative and simplified proofs of some of the main results of Deza and Onn.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
