In Mizera (J High Energy Phys 8:097, 2017) , Sebastian Mizera discovered a tree expansion formula of a homology intersection number on the configuration space \(\mathcal {M}_{0,n}\). The formula originates in a study of Kawai–Lewellen–Tye relation in string theory. In this paper, we give an elementary proof of the formula. The basic ingredients are the combinatorics of the real moduli space \(\overline{\mathcal {M}}_{0,n}(\mathbb {R})\) and a combinatorial identity related to the face number of the associahedron.

中文翻译：

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配置空间上的同构交点数的树展开公式$$ \ mathcal {M} _ {0，n} $$ M 0，n

在Mizera（J High Energy Phys 8：097，2017）中，塞巴斯蒂安·米泽拉（Sebastian Mizera）在配置空间\（\ mathcal {M} _ {0，n} \）上发现了一个同源相交数的树展开公式。该公式源自对弦论中的Kawai–Lewellen–Tye关系的研究。在本文中，我们给出了公式的基本证明。基本成分是实模空间\（\ overline {\ mathcal {M}} _ {0，n}（\ mathbb {R}）\）的组合和与关联面体的面号相关的组合标识。