| 1. | Other enumeration problems lead us to the study of orbits of permutation groups .
其它的计数问题引导我们去研究置换群的轨道。 |
| 2. | The permutation group coset method in calculations of gauge field vertices
关于规范场顶角计算的置换群陪集简化方法 |
| 3. | Regular permutation group
正则置换群 |
| 4. | With each recursive step , cross products with one additional permutation group are formed
伴随每个递回步骤，会形成带有一个额外置换群的向量积。 |
| 5. | 4 . according to the property that all states of a certain cellular automata can build a permutation group , we can design block cipher based on this property
根据有些细胞自动机的所有状态可以构成一个循环群这一特点，指出了利用细胞自动机构造分组密码的方式。 |
| 6. | We start by forming an arraylist containing a set of arraylists , in which each of the constituent arraylists contains exactly one element of the first permutation group
我们开始形成包含一组arraylists的arraylist ，在其中，每个构成的arraylists正好包含第一个置换群的一个元素。 |
| 7. | The method used here is to recursively form cross products of the values stored in each of the gui - control - possible - value vectors we will call these vectors , " permutation groups "
此处使用的方法是递回形成储存在每个gui控制项可能值vectors中的值的积（我们称这些vectors为“置换群（ permutation group ） ” ） 。 |
| 8. | Then , a new arraylist is created which contains the cross product of the contents of each of the constituent arraylists of the super - arraylist with all of the elements in the second permutation group
然后，建立一个新的arraylist ，它包含每个（超级arraylist的）构成的arraylists的内容和第二个置换群的所有单元的向量积。 |
| 9. | Subsequently we analyze the isomorphism relationship between ergodic matrices and the corresponding permutation group . by defining the permutation symbol operation system of ergodic matrices , we constructed a union form to express all existed permutation algorithms
通过在理论上分析遍历矩阵和置换群的同构关系，定义了遍历矩阵对应的置换运算和符号体系，再统一的框架下表达各种图像置乱变换。 |
| 10. | As to cyclic codes over finite chain rings , we study their stucture and develop the fourier transform method to finite chain rings . the permutation groups of cyclic codes and their extended codes are investigated using their mattson - solomn polynomials
对于有限链环上的循环码，我们研究了它们的结构，并把傅立叶变换的方法推广到有限链环，用循环码的mattson - solomn多项式对循环码及其扩展码的置换群进行了研究。 |
