Proofs and applications for a combinatorial identity
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摘要: 分别用复变函数论、组合论和图论三种方法证明了 与数\,$n^{n-2}$\,的组合计数问题相关的一个组合恒等式, 并给出该恒等式在图论、超平面配置等一些组合问题上的应用.Abstract: This paper considered a combinatorial identity related to some combinatorial enumeration problems involving the number $n^{n-2}$. The identity was proved in three different ways, which were in the theory of functions of complex variables, in graph theory, and in combinatorics, respectively. Finally, the identity was applied to enumerate certain kind of graphs and also the admissible sign types of type A.
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Key words:
- combinatorial identity /
- proofs /
- applications
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