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.2400
Bijective Proofs of Partition Identities of MacMahon, Andrews, and Subbarao

Authors: Shishuo Fu 1; James Sellers 2

  • 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.

https://doi.org/10.46298/dmtcs.2400
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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