环$\mathbb Q$上两个多项式差的最小次数第II部分：Davenport-Zannier对
Minimum Degree of the Difference of Two Polynomials over $\mathbb Q$. Part II: Davenport-Zannier pairs
摘要：
本文研究具有给定分解模式的多项式对，并使它们的差阶达到最小。我们称这样的多项式对为达文波特-赞尼尔对，或简称为DZ对。本文主要研究有理系数DZ-偶。在前面的论文中，在Dessins d 'enfants理论的框架下，我们建立了DZ-对和加权双色平面树之间的对应关系。这些是双色的平面树，其边缘被赋予正整数权重。当这样的树由其顶点的黑白度的集合唯一确定时，它被称为酉树，并且相应的DZ-对被定义在$\mathbb Q$上。在我们之前的论文中，我们对所有的幺正树进行了分类。在本文中，我们计算所有相应的多项式。在本文的最后一部分，我们提出了一些额外的材料有关的伽罗瓦论的DZ-对和加权树。
英文摘要：
In this paper we study pairs of polynomials with a given factorization pattern and such that the degree of their difference attains its minimum. We call such pairs of polynomials Davenport--Zannier pairs, or DZ-pairs for short. The paper is devoted to the study of DZ-pairs with rational coefficients. In our earlier paper, in the framework of the theory of dessins d'enfants, we established a correspondence between DZ-pairs and weighted bicolored plane trees. These are bicolored plane trees whose edges are endowed with positive integral weights. When such a tree is uniquely determined by the set of black and white degrees of its vertices, it is called unitree, and the corresponding DZ-pair is defined over $\mathbb Q$. In our earlier paper, we classified all unitrees. In this paper, we compute all the corresponding polynomials. In the final part of the paper we present some additional material concerning the Galois theory of DZ-pairs and weighted trees.
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