地图上的纽结置换

The Knot Permutation for Maps

将平面图的每条边赋予正负号后,能够将平面图转换成纽结,给出这种转换方法的代数性质:与转换方法相适应的变换规则是地图基础集上的纽结置换,对基础集上的地图进行两次纽结置换后得到原先的地图.将对偶运算和纽结置换结合起来,得到阶为3的复合置换.

A plane graph with each edge is assigned a positive or negative sign can be transformed into a knot.In this paper,algebraic properties of transformation method are given:transformation rules which adapt to the conversion method is basic knot permutation on the ground set of maps,the maps can be transformation into itself by two knot permu-tations.To combine dual operation and knot permutation,the compound permutation that order is three is given.