Relations of formal power series of one variable and coding of space curves by iterated path integrals

由两个字母X，Y和它们的反义词组成的单词在代数中构成了一个群结构，其中单词的连接是乘积。该组的一个元素定义了一个顶点在积分格上的多边形路径。平面曲线被认为是这种线性路径的概括，因此有X，Y等词。从这一观点出发，研究了平面曲线群，特别是将曲线表示为X、Y的广义词，并将其对数作为X、Y生成的自由代数的元进行了研究，得到了一些结果。

The words consisting of two letters X,Y and their inverses constitute a group structure in algebra, where the concatenation of words is the product. An element of this group defines a polygonal path with vertices on the integral lattice. Plane curves are regarded as generalization of such linear paths, hence words of X,Y. From this point of view, the group of plane curves are investigated, especially curves are presented as generalized words of X,Y and the logarithms of those curves are investigated as elements of the free algebra generated by X,Y, and some results are obtained.