关于“级别婚”的数学分析

Mathematical Analysis of the Hieratical Marriage

介绍了19世纪存在于澳大利亚土著中的一种婚姻形式—级别婚,从群论的角度说明级别婚的三种主要形式都对应于一个对称群,从而可以用几何方法形象的表示这种婚姻形式;进而,从对称的观点说明婚姻形式从简单到复杂的演化过程,代数上对应于对称群阶数的增加,几何上则对应于对称性的加强.

This article introduces a kind of marriage-hieratical marriage which existed in aboriginals in Australia in the 19th century. It demonstrates that this kind of marriage corresponds to a symmetric group from the perspective of group in mathematics, thus shows geometrically the three kinds of hieratical marriage. Furthermore, it illustrates when the form of marriage changes from simplicity to complexity, the group has better symmetry on geometry, the order of the group is higher, but it is still a symmetric group.