显示找到的3个结果中的1-3个。
第页1
0, 1, 1, 2, 0, 2, 3, 4, 3, 3, 4, 5, 0, 2, 4, 5, 2, 1, 5, 5, 5, 6, 3, 5, 4, 1, 4, 6, 7, 7, 4, 0, 0, 3, 7, 7, 8, 6, 12, 1, 3, 2, 8, 6, 8, 9, 10, 13, 13, 2, 1, 9, 10, 9, 9, 10, 11, 14, 12, 18, 0, 10, 11, 6, 8, 10, 11, 8, 15, 16, 19, 19, 11, 8, 7, 11, 11, 11, 12, 9, 16, 17, 20, 18, 0, 9, 11, 10, 7, 10, 12, 13, 18, 17, 14, 21, 22, 1, 1, 10, 6, 6, 9, 13, 13, 14, 19, 6, 15, 22, 23, 2, 0, 14, 7, 9, 8, 14, 12, 14
评论
方阵A(行>=0,列>=0)由向下反对偶读取为:A(0,0),A(0,1),A。。。
A(i,j)给出了等级(按表中使用的顺序)A055089号)由不规则表中列为i-th和j-th排列的排列p和q合成得到的排列A055089号(注意,身份置换是第0个)。这里的约定是“左置换作用”,因此,如果p1和p2是置换,则p1和p2(p1*p2)的乘积定义为i=1。。。
每一行和每一列都是A001477号,因为这是无限可枚举群的Cayley表(“乘法表”),即无限对称群(S_inf)的子群,它由只移动有限个元素的置换组成。
例子
数组的左上角:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, ...
1, 0, 4, 5, 2, 3, 7, 6, 10, 11, 8, 9, 18, ...
2, 3, 0, 1, 5, 4, 12, 13, 14, 15, 16, 17, 6, ...
3, 2, 5, 4, 0, 1, 13, 12, 16, 17, 14, 15, 19, ...
4, 5, 1, 0, 3, 2, 18, 19, 20, 21, 22, 23, 7, ...
5, 4, 3, 2, 1, 0, 19, 18, 22, 23, 20, 21, 13, ...
6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 14, ...
7, 6, 10, 11, 8, 9, 1, 0, 4, 5, 2, 3, 20, ...
8, 9, 6, 7, 11, 10, 14, 15, 12, 13, 17, 16, 0, ...
9, 8, 11, 10, 6, 7, 15, 14, 17, 16, 12, 13, 21, ...
10, 11, 7, 6, 9, 8, 20, 21, 18, 19, 23, 22, 1, ...
11, 10, 9, 8, 7, 6, 21, 20, 23, 22, 18, 19, 15, ...
12, 13, 14, 15, 16, 17, 2, 3, 0, 1, 5, 4, 8, ...
...
对于A(1,2)(行=1,列=2,均从零开始),我们将在使用的顺序中秩为1的置换p作为置换A055089号,这是一个简单的换位(12),我们可以用固定项来扩展它(如{2,1,3,4,5,…}),作为置换q,我们采用秩为2的置换(在同一列表中),即{1,3,2}。我们从左边把它们组合起来,这样后一个q首先作用,因此c(i)=p(q(i)),结果是置换{2,3,1},它在A055089号因此A(1,2)=4。
对于A(2,1),我们以相反的顺序组成这两个排列,如d(i)=q(p(i)),这给出了排列{3,1,2},它被列为A055089号因此A(2,1)=3。
0, 1, 1, 2, 0, 2, 3, 3, 4, 3, 4, 2, 0, 5, 4, 5, 5, 5, 1, 2, 5, 6, 4, 1, 4, 5, 3, 6, 7, 7, 3, 0, 0, 4, 7, 7, 8, 6, 8, 2, 3, 1, 12, 6, 8, 9, 9, 10, 9, 1, 2, 13, 13, 10, 9, 10, 8, 6, 11, 10, 0, 18, 12, 14, 11, 10, 11, 11, 11, 7, 8, 11, 19, 19, 16, 15, 8, 11, 12, 10, 7, 10, 11, 9, 0, 18, 20, 17, 16, 9, 12, 13, 13, 9, 6, 6, 10, 1, 1, 22, 21, 14, 17, 18, 13, 14, 12, 14, 8, 9, 7, 14, 0, 2, 23, 22, 15, 6, 19, 14
例子
数组的左上角:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, ...
1, 0, 3, 2, 5, 4, 7, 6, 9, 8, 11, 10, 13, ...
2, 4, 0, 5, 1, 3, 8, 10, 6, 11, 7, 9, 14, ...
3, 5, 1, 4, 0, 2, 9, 11, 7, 10, 6, 8, 15, ...
4, 2, 5, 0, 3, 1, 10, 8, 11, 6, 9, 7, 16, ...
5, 3, 4, 1, 2, 0, 11, 9, 10, 7, 8, 6, 17, ...
6, 7, 12, 13, 18, 19, 0, 1, 14, 15, 20, 21, 2, ...
7, 6, 13, 12, 19, 18, 1, 0, 15, 14, 21, 20, 3, ...
8, 10, 14, 16, 20, 22, 2, 4, 12, 17, 18, 23, 0, ...
9, 11, 15, 17, 21, 23, 3, 5, 13, 16, 19, 22, 1, ...
10, 8, 16, 14, 22, 20, 4, 2, 17, 12, 23, 18, 5, ...
11, 9, 17, 15, 23, 21, 5, 3, 16, 13, 22, 19, 4, ...
12, 18, 6, 19, 7, 13, 14, 20, 0, 21, 1, 15, 8, ...
...
1, 0, 5, 4, 3, 2, 7, 6, 11, 10, 9, 8, 19, 18, 23, 22, 21, 20, 13, 12, 17, 16, 15, 14, 25, 24, 29, 28, 27, 26, 31, 30, 35, 34, 33, 32, 43, 42, 47, 46, 45, 44, 37, 36, 41, 40, 39, 38, 49, 48, 53, 52, 51, 50, 55, 54, 59, 58, 57, 56, 67, 66, 71, 70, 69, 68, 61, 60, 65, 64, 63, 62, 97, 96, 101, 100, 99, 98, 103, 102, 107, 106, 105, 104, 115, 114, 119, 118, 117, 116, 109, 108, 113, 112, 111, 110, 73
评论
从列表中取第n个(n>=0)置换A060117号,将1更改为2,将2更改为1以获得另一个置换,并注意其在同一列表中的秩以获得a(n)。
非负整数的自逆置换。
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