论文标题
在矩形交换转换组上
On groups of rectangle exchange transformations
论文作者
论文摘要
我们研究了每个维度d> 0的间隔交换转换组的IET = REC_1的概括REC_D，称为矩形交换转换组。 IET中限制旋转的子集是一个生成子集，我们证明这些元素的自然概括（称为限制的散装）形成了REC_D的生成子集。我们用T_D表示REC_D的子集由这些转换组成，这些转换由翻译置于两个不相交的矩形。我们证明REC_D的派生子组由T_D生成。我们还标识了rec_d的abelianization。
We study a generalization Rec_d of the group IET=Rec_1 of interval exchange transformations in every dimension d>0, called the rectangle exchange transformations group. The subset of restricted rotations in IET is a generating subset and we prove that a natural generalization of these elements, called restricted shuffles, form a generating subset of Rec_d. We denote by T_d the subset of Rec_d made up of those transformations that permute two disjoint rectangles by translations. We prove that the derived subgroup of Rec_d is generated by T_d. We also identify the abelianization of Rec_d.
