| 树的计数 |
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| 引用本文： | 王彦辉,方腾. 树的计数[J]. 数学的实践与认识, 2014, 0(10) |
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| 作者姓名： | 王彦辉 方腾 |
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| 作者单位： | 桂林航天工业高等专科学校信息工程系;北京大学数学科学学院; |
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| 摘 要： | 阶数为n且不同构的树的个数称为树列t_n.对n阶错排做了划分,汇总计算了对称群的循环指数,结合树的结构特性和波利亚计数定理,给出了一种确定t_n的算法并证明了算法的合理性.计算表明,树列t_n={1,1,1,2,3,6,11,23,47,106,235,551,…}.
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| 关 键 词： | 树列 置换群 波利亚计数 图论 树 |
The Counting of Trees |
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| Abstract: | In the meaning of isomorphism,the numbers of the tree with order n is called the sequence of trees,which is denoted by t_n.actorized on the n-derangement,the cycle index of symmetry group is obtained.By the constructional properties of the tree and the Polya counting formula,this paper provides a method to determine t_nnd finds that t_n {1,1,1,2,3,6,11,23,47,106,235,551,…}. |
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| Keywords: | sequence of trees permutation group Polya's counting graph theory tree |
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