平面图的Feynman恒等式
Feynman identity for planar graphs
摘要：
平面图的费曼恒等式（FI）将图的欧拉多项式与图中闭非周期符号圈的等价类上的无穷乘积联系起来。本文的主要目标是计算给定长度和符号的平面图中的非周期循环的等价类的数目，并解释自由李超代数的背景下的FI编码的数据。这解决了平面图的情况下，首先提出的问题S。Sherman，并将FI设为由图生成的自由李超代数的分母单位元。得到了其它结果。例如，与图形的zeta函数有关。
英文摘要：
The Feynman identity (FI) of a planar graph relates the Euler polynomial of the graph to an infinite product over the equivalence classes of closed nonperiodic signed cycles in the graph. The main objectives of this paper are to compute the number of equivalence classes of nonperiodic cycles of given length and sign in a planar graph and to interpret the data encoded by the FI in the context of free Lie superalgebras. This solves in the case of planar graphs a problem first raised by S. Sherman and sets the FI as the denominator identity of a free Lie superalgebra generated from a graph. Other results are obtained. For instance, in connection with zeta functions of graphs.
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