着色的等价类
Equivalence Classes of Colorings
摘要：
对于任何链路和任何模$m$，我们引入一个等价关系的一组非平凡的m-染色的链接（一个m-染色的值在Z/mZ）。给定一个链路图，非平凡m-着色的等价类是由图中弧的颜色分配形成的，这些弧是由前一个着色通过在每个交叉处保持着色条件的弧中的颜色置换获得的。这个要求意味着等价类的拓扑不变性。我们表明，对于一个素数模的等价类的数量取决于模和染色矩阵的秩（相对于这个模）。
英文摘要：
For any link and for any modulus $m$ we introduce an equivalence relation on the set of non-trivial m-colorings of the link (an m-coloring has values in Z/mZ). Given a diagram of the link, the equivalence class of a non-trivial m-coloring is formed by each assignment of colors to the arcs of the diagram that is obtained from the former coloring by a permutation of the colors in the arcs which preserves the coloring condition at each crossing. This requirement implies topological invariance of the equivalence classes. We show that for a prime modulus the number of equivalence classes depends on the modulus and on the rank of the coloring matrix (with respect to this modulus).
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