• Journal for History of Mathematics
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• v.19 no.1
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• pp.33-42
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• 2006

In this paper, we study the theoretical and historical backgrounds with respect to isomorphism problem of combinatorial objects which is one of major problems in the theory of Combinatorics. And also, we introduce a partial result for isomorphism problem of Cayley objects over a finite field.

• Journal for History of Mathematics
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• v.21 no.3
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• pp.127-142
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• 2008

In this paper, we introduce four different approaches of proving Cayley formula, which counts the number of trees(acyclic connected simple graphs). The first proof was done by Cayley using recursive formulas. On the other hands the core idea of the other three proofs is the bijective method-find an one to one correspondence between the set of trees and a suitable family of combinatorial objects. Each of the three bijection gives its own generalization of Cayley formula. In particular, the last proof, done by Seo and Shin, has an application to computer science(theoretical computation), which is a typical example that pure mathematics supply powerful tools to other research fields.