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Bijective Proofs of Partition Identities of MacMahon, Andrews, and Subbarao

Abstract : We revisit a classic partition theorem due to MacMahon that relates partitions with all parts repeated at least once and partitions with parts congruent to $2,3,4,6 \pmod{6}$, together with a generalization by Andrews and two others by Subbarao. Then we develop a unified bijective proof for all four theorems involved, and obtain a natural further generalization as a result.
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https://hal.inria.fr/hal-01207610
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Shishuo Fu, James Sellers. Bijective Proofs of Partition Identities of MacMahon, Andrews, and Subbarao. 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), 2014, Chicago, United States. pp.289-296. ⟨hal-01207610⟩

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