Shishuo Fu ; James Sellers
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Bijective Proofs of Partition Identities of MacMahon, Andrews, and Subbarao
dmtcs:2400 -
Discrete Mathematics & Theoretical Computer Science,
January 1, 2014,
DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)
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https://doi.org/10.46298/dmtcs.2400
Bijective Proofs of Partition Identities of MacMahon, Andrews, and Subbarao
Authors: Shishuo Fu 1; James Sellers 2
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Shishuo Fu;James Sellers
1 Chongqing University (CHINA)
2 Pennsylvania State University
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.