论文标题
接触等效性的配置多项式
Configuration polynomials under contact equivalence
论文作者
论文摘要
配置多项式概括了由图定义的经典Kirchhoff多项式。他们的研究阐明了Feynman Integrands中出现的某些多项式。接触等效性提供了一种研究相关配置超表面的方法。在任何配置多项式的接触等效类中，我们识别一个多项式，变量数量最少。它是一个多项式配置。这个最小数字由$ r+1 \选择2 $界定，其中$ r $是基础矩阵的等级。我们表明，等价类的数量完全有限至排名$ 3 $，并列出这些类别的明确正常表格。
Configuration polynomials generalize the classical Kirchhoff polynomial defined by a graph. Their study sheds light on certain polynomials appearing in Feynman integrands. Contact equivalence provides a way to study the associated configuration hypersurface. In the contact equivalence class of any configuration polynomial we identify a polynomial with minimal number of variables; it is a configuration polynomial. This minimal number is bounded by $r+1\choose 2$, where $r$ is the rank of the underlying matroid. We show that the number of equivalence classes is finite exactly up to rank $3$ and list explicit normal forms for these classes.
