群的轮换指标与Polya理论

The Rotated Index Signs of the Cluster and the Theories of Polya

文章从置换的轮换指标出发,引用第一类Stirling数S1(n,k),证明了∑λ1+2λ2+…nλn=n1λ1!λ2!…λn!1λ12λ2…nλn=1,∑λ1+2λ2+…nλn=n(-1)λ1+2λ2+…nλnλ1!λ2!…λn!1λ12λ2…nλn=0.应用旋转群的概念,导出正八面体的顶点,边,面的轮换指标,并在Polya理论下,根据等价函数类和推广等价函数类的概念,讨论了其轨道个数的计算.

The paper discusses the total yokes of Sn＇s rotated index signs （λ1,λ2,…λn）, quotes the first stirling number S]（n, k）, proves the formula λ1＋2λ2∑＋…nλn=1/nλ1!λ2!…λn!1^λ12^λ2…n^λn=1,λ1＋2λ2∑＋…nλn=（-1）λ1＋2λ2＋…nλn/nλ1!λ2!…λn!1^λ12^λ2…n^λn=0and applies the concept of the revolves cluster, and leads the top of the positive octahedron, side, face of the rotated index signs. Under the Polya theories, according to the concept of equal function and the expansion function kinds, the calculation of its orbit piece is discussed.