The $c_2$-invariant is an arithmetic graph invariant useful for understanding Feynman periods. Brown and Schnetz conjectured that the $c_2$-invariant has a particular symmetry known as completion invariance. This paper will prove completion invariance of the $c_2$-invariant in the $p=2$ case, extending previous work of one of us. The methods are combinatorial and enumerative involving counting certain partitions of the edges of the graph.

中文翻译：

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完成 $p=2$ 的 $c_2$ 完成猜想

$c_2$-不变量是一个算术图不变量，有助于理解费曼周期。Brown 和 Schnetz 推测 $c_2$ 不变量具有称为完成不变性的特殊对称性。本文将证明 $p=2$ 情况下 $c_2$ 不变性的完成不变性，扩展我们其中一个人之前的工作。这些方法是组合的和枚举的，涉及计算图形边缘的某些分区。