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首页> 外文期刊>Journal of Combinatorial Theory, Series B >DICHROMATIC SUMS REVISITED
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DICHROMATIC SUMS REVISITED

机译：重新审视了二种子动量

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In a previous paper the author studied an enumerating power series Phi in six variables. The typical term was the sum of a dichromatic polynomial over all rooted planar maps of given numbers of vertices and faces and given valencies for the root face and root vertex. Loops and multiple joins were allowed. The polynomial was the one now commonly called the ''Tutte polynomial'' by other writers. An equation for Phi was obtained. It made possible a recursive calculation of coefficients in the order of increasing edge number. The present paper arose out of the observation that the equation for Phi takes a particularly simple form when;he variables x and y of the dichromatic polynomial are each given the value 1. The value of the polynomial is then the number of spanning trees of the map concerned. In that special case a theoretical solution is obtained. It is stated in terms of a remainder obtained when a certain power series in the four remaining variables, slightly transformed, is divided by a certain polynomial. (C) 1996 Academic Press, Inc. [References: 3]
机译：在上一篇论文中，作者在六个变量中研究了一个枚举电源系列phi。典型术语是给定数量的顶点和面部的所有生根平面图和根面和根顶点的给定价的二色多项式的总和。允许循环和多个连接。多项式是现在通常被其他作家称为“Tutte多项式”的人。获得了PHI的等式。它使得在增加边缘数量的顺序中可能对系数进行递归计算。本文出现了观察结果，即PHI的等式采用特别简单的形式。当何种变量x和二色多项式的变量x和y各自给出了值1.多项式的值是跨越树的数量地图有关。在这种特殊情况下，获得理论解决方案。就当四个剩余变量中的某个功率系列略微转化时，就剩余的剩余部分而言，其术语术语。 （c）1996年学术出版社，Inc。[参考文献：3]

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