论文标题
外太空作为Cutkosky规则和共同体的组合主链
Outer Space as a combinatorial backbone for Cutkosky rules and coactions
论文作者
论文摘要
我们认为对于任何无桥图都存在的共有。它是基于与任何此类图相关的立方链复合物，考虑了两个边界操作：缩小边缘或去除它们。只有当图$ g $的跨越树的数量等于其内部边缘的数量时，我们才能发现此处构建的图形coaction $δ^g $与Britto and Collaborators提出的coaction $δ_{\ Mathsf {inc}} $一致。这种情况的图是一环图形或它们的二元组，多边的香蕉图。他们提供了迄今为止Britto和合作者讨论的唯一示例。我们称此类图表简单图形。 Dunce的帽子图是第一个非简单图形。其跨树（五）的数量超过其边缘的数量（四）。我们比较了确实不同意并讨论这一结果的两个共同体。我们还指出，对于运动学重归其化方案，coaction $δ^g $简化。
We consider a coaction which exists for any bridge-free graph. It is based on the cubical chain complex associated to any such graph by considering two boundary operations: shrinking edges or removing them. Only if the number of spanning trees of a graph $G$ equals its number of internal edges we find that the graphical coaction $Δ^G$ constructed here agrees with the coaction $Δ_{\mathsf{Inc}}$ proposed by Britto and collaborators. The graphs for which this is the case are one-loop graphs or their duals, multi-edge banana graphs. They provide the only examples discussed by Britto and collaborators so far. We call such graphs simple graphs. The Dunce's cap graph is the first non-simple graph. The number of its spanning trees (five) exceeds the number of its edges (four). We compare the two coactions which indeed do not agree and discuss this result. We also point out that for kinematic renormalization schemes the coaction $Δ^G$ simplifies.
