图特多项式的推广

Pub Date : 2018-10-11 DOI:10.3792/pjaa.95.111

T. Miezaki, M. Oura, Tadashi Sakuma, Hidehiro Shinohara

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引用次数: 3

摘要

本文引入了属$g$的Tutte多项式的概念，并讨论了它的一些性质。我们注意到，属1的图特多项式是众所周知的图特多项式。图特多项式是类矩阵不变量，并且我们证明格$g$的图特多项式也是类矩阵不变量。本文和即将发表的论文的主要结果表明，格$g$的Tutte多项式是完全的矩阵不变量。

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A generalization of the Tutte polynomials

In this paper, we introduce the concept of the Tutte polynomials of genus $g$ and discuss some of its properties. We note that the Tutte polynomials of genus one are well-known Tutte polynomials. The Tutte polynomials are matroid invariants, and we claim that the Tutte polynomials of genus $g$ are also matroid invariants. The main result of this paper and the forthcoming paper declares that the Tutte polynomials of genus $g$ are complete matroid invariants.

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