显示找到的9个结果中的1-9个。
第页1
1, 1, 2, 4, 10, 26, 74, 218, 672, 2134, 6964, 23206, 78724, 271014, 944766, 3328872, 11838378, 42441326, 153236900, 556746772, 2034098988
评论
相应的自同构将集合划分到的轨道数A000108号(n) 具有n个内部节点的二叉树。
1, 1, 2, 3, 6, 12, 30, 79, 232, 716, 2318, 7714, 26270, 90944, 319146, 1132185, 4053618, 14626828, 53136324, 194174324, 713267792
0, 1, 0, 2, 1, 0, 3, 3, 1, 0, 4, 2, 2, 1, 0, 5, 7, 3, 2, 1, 0, 6, 8, 4, 3, 2, 1, 0, 7, 6, 6, 5, 3, 2, 1, 0, 8, 5, 5, 4, 5, 3, 2, 1, 0, 9, 4, 7, 6, 6, 6, 3, 2, 1, 0, 10, 17, 8, 7, 4, 5, 6, 3, 2, 1, 0, 11, 18, 9, 8, 7, 4, 4, 4, 3, 2, 1, 0, 12, 20, 11, 12, 8, 7, 5, 5, 4, 3, 2, 1, 0, 13, 21, 14, 13, 12
评论
第n行是从表中的第n个非递归自同构获得的加泰罗尼亚自同构的签名置换A089840号使用递归方案“SPINE”。在这个递归方案中,给定的自同构首先应用于二叉树的根,然后算法递归到新的右侧分支。相关的方案将处理脊椎和!SPINE可用于从任何构造性或破坏性实现的自同构中获得这样的转换自同构。此表中每行只出现一次。这些排列的倒数可以在表中找到A122204号.
递归方案SPINE有一个定义良好的逆,即它在所有加泰罗尼亚自同构集上充当双射映射。具体地说,如果g=SPINE(f),那么(f s)=(cond((pair?s)(let(t(g s)))(cons(car t)(g^{-1}(cdr t))))。这意味着对于表中的任何非递归自同构fA089840号,脊椎^{-1}(f)也位于A089840号,这又意味着表的行A089840号形成此表行的(适当的)子集。
参考文献
A.Karttunen,正在准备论文,可通过电子邮件获取草稿。
黄体脂酮素
(方案:)(define(SPINE foo)(letrec((bar(lambda(s)(let(t(foo))))(if(pair?t)(cons(car t)(bar(cdr t)))bar)))
(定义(!SPINE foo!)(letrec((bar!(lambda(s)(cond((pair?s)(foo!s)(ba!(cdr s))))bar!))
交叉参考
参见本表前22行:第0行(身份置换):A001477号, 1:A069767号, 2:A057509号, 3:A130341号, 4:A130343号, 5:130345美元, 6:A130347号, 7:A122282号, 8:A082339号, 9:A130349号, 10:130351美元, 11:A130353号, 12:A074685号, 13:130355美元, 14:A130357号, 15:130359英镑, 16:A130361号, 17:A057501号, 18:A130363号, 19:A130365型, 20:A130367号, 21:A069770号.其他行:第251行:A089863号,第253行:A123717号,第3608行:A129608号,第3613行:A072796号,第65352行:A074680号,第79361行:A123715号.
0, 1, 0, 2, 1, 0, 3, 3, 1, 0, 4, 2, 2, 1, 0, 5, 7, 3, 2, 1, 0, 6, 8, 4, 3, 2, 1, 0, 7, 6, 5, 4, 3, 2, 1, 0, 8, 4, 7, 5, 4, 3, 2, 1, 0, 9, 5, 6, 6, 5, 4, 3, 2, 1, 0, 10, 17, 8, 8, 8, 5, 4, 3, 2, 1, 0, 11, 18, 9, 7, 6, 8, 5, 5, 3, 2, 1, 0, 12, 20, 10, 9, 7, 7, 7, 4, 4, 3, 2, 1, 0, 13, 21, 12, 10, 9, 6
交叉参考
参见本表前22行:第0行(身份置换):A001477号, 1:A082345号, 2:A130936号, 3:A073288号, 4:A130942号, 5:A130940型, 6:A130938号, 7:A130944号, 8:A130946号, 9:A130952号, 10:A130950型, 11:A130948号, 12:A057161号, 13:A130962号, 14:A130964号, 15:A069767号, 16:A130966号, 17:A074688美元, 18:A130954号, 19:A130956号, 20:A130960型, 21:A130958号,其他行:169:A069770号, 3617:A082339号, 65167:A057501号.
0, 1, 2, 3, 4, 5, 7, 6, 8, 9, 10, 12, 11, 13, 17, 18, 16, 14, 15, 20, 19, 21, 22, 23, 24, 26, 25, 27, 31, 32, 30, 28, 29, 34, 33, 35, 36, 45, 46, 49, 48, 50, 44, 47, 42, 37, 38, 43, 39, 40, 41, 54, 55, 53, 51, 52, 57, 56, 58, 59, 61, 60, 62, 63, 64, 65, 66, 68, 67, 69
黄体脂酮素
(在列表结构上实现此自同构的Scheme函数:)
(定义(gma082340!s)(条件((对)(gma02340!(cdr))(gma 072797!s)))
0, 1, 2, 3, 4, 5, 7, 6, 8, 9, 10, 12, 11, 13, 17, 18, 16, 14, 15, 20, 21, 19, 22, 23, 24, 26, 25, 27, 31, 32, 30, 28, 29, 34, 35, 33, 36, 45, 46, 48, 49, 50, 44, 47, 42, 37, 38, 43, 39, 40, 41, 54, 55, 57, 58, 59, 53, 56, 51, 52, 61, 62, 63, 60, 64, 65, 66, 68, 67, 69
黄体脂酮素
(在列表结构上实现此自同构的Scheme函数:)
(定义(gma082341!s)
0, 1, 2, 3, 4, 5, 7, 6, 8, 9, 10, 12, 11, 13, 17, 18, 16, 14, 15, 21, 19, 20, 22, 23, 24, 26, 25, 27, 31, 32, 30, 28, 29, 35, 33, 34, 36, 45, 46, 48, 49, 50, 44, 47, 42, 37, 38, 43, 39, 40, 41, 58, 59, 56, 51, 52, 57, 53, 54, 55, 63, 60, 61, 62, 64, 65, 66, 68, 67, 69
黄体脂酮素
(在列表结构上实现此自同构的Scheme函数:)
(定义(gma082342!s)
0, 1, 2, 3, 4, 5, 7, 6, 8, 9, 10, 11, 12, 13, 17, 18, 16, 14, 15, 20, 21, 19, 22, 23, 24, 26, 25, 27, 28, 29, 30, 31, 32, 33, 35, 34, 36, 45, 46, 49, 48, 50, 44, 47, 42, 37, 38, 43, 40, 39, 41, 54, 55, 57, 58, 59, 53, 56, 51, 52, 61, 62, 63, 60, 64, 65, 66, 67, 68, 69, 73, 74
0, 1, 2, 3, 4, 5, 7, 6, 8, 9, 10, 11, 12, 13, 17, 18, 16, 14, 15, 20, 19, 21, 22, 23, 24, 26, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 45, 46, 49, 48, 50, 44, 47, 42, 37, 38, 43, 40, 39, 41, 54, 55, 53, 51, 52, 57, 56, 58, 59, 61, 60, 62, 63, 64, 65, 66, 67, 68, 69, 73, 74
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