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An Extension of Euler’s Theorem


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1 Centre for Advanced Study in Mathematics, Panjab University, Chandigarh-160014, India
     

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Euler’ s classical partition identity “The number of partitions of an integer v into distinct parts is equal to the number of its partitions into odd parts” is extended to eight more combinatorial functions. This results in a 10-way combinatorial identity which implies 45 combinatorial identities in the usual sense. Euler’s identity is just one of them.
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  • An Extension of Euler’s Theorem

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Authors

A. K. Agarwal
Centre for Advanced Study in Mathematics, Panjab University, Chandigarh-160014, India

Abstract


Euler’ s classical partition identity “The number of partitions of an integer v into distinct parts is equal to the number of its partitions into odd parts” is extended to eight more combinatorial functions. This results in a 10-way combinatorial identity which implies 45 combinatorial identities in the usual sense. Euler’s identity is just one of them.