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

Shishuo Fu; James Sellers

doi:10.46298/dmtcs.2400

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 SubbaraoConference paper

Authors: Shishuo Fu ^1,²; James Sellers ³

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: partition,residue classes,bijection,generating function,[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]

Shishuo Fu ; James Sellers - Bijective Proofs of Partition Identities of MacMahon, Andrews, and Subbarao

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