Journal of East China Normal University(Natural Sc ›› 2012, Vol. 2012 ›› Issue (1): 88-96.

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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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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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