论文标题
在兼容的集合中，Tutte多项式的扩展
On the compatible sets expansion of the Tutte polynomial
论文作者
论文摘要
Kochol（2021）使用\ emph {兼容集}的概念为矩阵的Tutte多项式提供了一个新的扩展公式，并询问该扩展与内部外部活动公式如何相关。在这里，我们提供了一个答案，该答案是作为Matroid Perspectives的Las Vergnas的Trivariate Tutte多项式的广义版本的特殊情况。 Kochol（2022和2023）与这项工作同时证明了对Matroid观点和对活动的生命的相同概括，但使用了不同的方法。 Kochol使用收缩 - 局部关系递归证明了这两种结果，而我们给出了更直接的两次培养证明，并使用它来推导LAS Vergnas活动扩展的兼容集扩展公式。
Kochol (2021) gave a new expansion formula for the Tutte polynomial of a matroid using the notion of \emph{compatible sets}, and asked how this expansion relates to the internal-external activities formula. Here, we provide an answer, which is obtained as a special case of a generalized version of the expansion formula to Las Vergnas's trivariate Tutte polynomials of matroid perspectives. The same generalization to matroid perspectives and bijection with activities have been independently proven by Kochol (2022 and 2023) in parallel with this work, but using different methods. Kochol proves both results recursively using the contraction-deletion relations, whereas we give a more direct proof of the bijection and use that to deduce the compatible sets expansion formula from Las Vergnas's activities expansion.
