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首页> 外文期刊>Journal of knot theory and its ramifications >TUTTE POLYNOMIALS OF TENSOR PRODUCTS OF SIGNED GRAPHS AND THEIR APPLICATIONS IN KNOT THEORY
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TUTTE POLYNOMIALS OF TENSOR PRODUCTS OF SIGNED GRAPHS AND THEIR APPLICATIONS IN KNOT THEORY

机译：有符号图的张量积的图特特多项式及其在结理论中的应用

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摘要

It is well-known that the Jones polynomial of an alternating knot is closely related to the Tutte polynomial of a special graph obtained from a regular projection of the knot. Relying on the results of Bollobas and Riordan, we introduce a generalization of Kauffman's Tutte polynomial of signed graphs for which describing the effect of taking a signed tensor product of signed graphs is very simple. We show that this Tutte polynomial of a signed tensor product of signed graphs may be expressed in terms of the Tutte polynomials of the original signed graphs by using a simple substitution rule. Our result enables us to compute the Jones polynomials of some large non-alternating knots. The combinatorics used to prove our main result is similar to Tutte's original way of counting "activities" and specializes to a new, perhaps simpler proof of the known formulas for the ordinary Tutte polynomial of the tensor product of unsigned graphs or matroids.
机译：众所周知，交替结的琼斯多项式与从结的正则投影获得的特殊图的Tutte多项式密切相关。依靠Bollobas和Riordan的结果，我们引入了Kauffman签名图的Tutte多项式的推广，对于描述采用签名图的签名张量积的效果非常简单。我们表明，通过使用简单的替换规则，可以用原始符号图的Tutte多项式来表示符号图的符号张量积的这个Tutte多项式。我们的结果使我们能够计算一些大的非交替结的琼斯多项式。用于证明我们的主要结果的组合函数类似于Tutte最初计算“活动”的方式，并且专门研究了无符号图或拟阵的张量积的普通Tutte多项式的已知公式的一种新的，也许更简单的证明。

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