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ON A COMBINATORIAL PROOF FOR AN IDENTITY INVOLVING THE TRIANGULAR NUMBERS

Part of: Combinatorics

Published online by Cambridge University Press:  27 September 2010

JOSE PLÍNIO O. SANTOS  and
ROBSON DA SILVA
JOSE PLÍNIO O. SANTOS
Affiliation:
IMECC-UNICAMP, C.P. 6065, 13084-970 Campinas-SP, Brazil (email: [email protected])
ROBSON DA SILVA*
Affiliation:
ICE-UNIFEI, C.P. 50, 37500-903 Itajubá-MG, Brazil (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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In this paper, we present a combinatorial proof for an identity involving the triangular numbers. The proof resembles Franklin’s proof of Euler’s pentagonal number theorem.

Keywords

partition identitiescombinatoricsFerrers graph

MSC classification

Secondary: 05A19: Combinatorial identities, bijective combinatorics
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 83 , Issue 1 , February 2011 , pp. 46 - 49
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

References

[1]Andrews, G. E., ‘Enumerative proofs of certain q-identities’, Glasg. Math. J. 8 (1967), 33–40.CrossRefGoogle Scholar
[2]Andrews, G. E., The Theory of Partitions, Encyclopedia of Mathematics and its Applications, 2 (ed. Rota, G.-C.) (Addison-Wesley, Reading, MA, 1976).Google Scholar
[3]Brietzke, E. H. M., Santos, J. P. O. and Silva, R., ‘Bijective proofs using two-line matrix representations for partitions’, Ramanujan J., accepted.Google Scholar