A Unification of Two Refinements of Euler's Partition Theorem

William Y.C. Chen, Henry Y. Gao, Kathy Q. Ji and Martin Y.X. Li

Dedicated to Professor George Andrews on the Occasion of His Seventieth Birthday.

  Abstract:  We obtain a unification of two refinements of Euler's partition theorem respectively due to Bessenrodt and Glaisher. A specialization of Bessenrodt's insertion algorithm for a generalization of the Andrews-Olsson partition identity is used in our combinatorial construction.

  AMS Classification:  05A17, 11P81

  Keywords:  partition, Euler's partition theorem, refinement, bijection, Bessenrodt's bijection, Andrews-Olsson's theorem

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