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Discrete Mathematics & Theoretical Computer Science |
Shishuo Fu ; James Sellers - 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) - https://doi.org/10.46298/dmtcs.2400Bijective Proofs of Partition Identities of MacMahon, Andrews, and SubbaraoArticle
- 1 Chongqing University (CHINA)
- 2 Chongqing University [Chongqing]
- 3 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.
Source: HAL:hal-01207610v1
Volume: DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)
Section: Proceedings
Published on: January 1, 2014
Imported on: November 21, 2016
Keywords: bijection,generating function,residue classes,partition,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]
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