华东师范大学学报(自然科学版) ›› 2012, Vol. 2012 ›› Issue (1): 88-96.

• 应用数学与基础数学 • 上一篇    下一篇

一个组合恒等式的证明和应用

时俭益1, 王 玮2   

  1. 1. 华东师范大学 数学系, 上海 200241;
    2. 上海市经济和信息化委员会信息中心, 上海 200003
  • 收稿日期:2010-03-01 修回日期:2010-06-01 出版日期:2012-01-25 发布日期:2012-01-26

Proofs and applications for a combinatorial identity

SHI Jian-yi 1, WANG Wei 2   

  1. 1.  Department of Mathematics, East China Normal University, Shanghai 200241,  China; 2.  Information Center, Shanghai Municipal Commission of
    Economy and Informization, Shanghai 200003,  China
  • Received:2010-03-01 Revised:2010-06-01 Online:2012-01-25 Published:2012-01-26

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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.

关键词: 组合恒等式, 证明, 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.

Key words: combinatorial identity, proofs, applications

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