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Register a new userA bijection for Eulers partition theorem in the spirit of Bressoud
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Authors
John Murray
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For each positive integer $n$, we construct a bijection between the odd partitions and the distinct partitions of $n$ which extends Bressouds bijection between the odd-and-distinct partitions of $n$ and the splitting partitions of $n$. We compare our bijection with the classical bijections of Glaisher and Sylvester, and also with a recent bijection due to Chen, Gao, Ji and Li.
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We obtain a unification of two refinements of Eulers partition theorem respectively due to Bessenrodt and Glaisher. A specialization of Bessenrodts insertion algorithm for a generalization of the Andrews-Olsson partition identity is used in our combinatorial construction.
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