Bijective proofs of partition identities of Macmahon, Andrews, and Subbarao

Shishuo Fu, James A. Sellers

Research output: Contribution to journalConference articlepeer-review


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 (mod 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.

Original languageEnglish (US)
Pages (from-to)289-295
Number of pages7
JournalDiscrete Mathematics and Theoretical Computer Science
StatePublished - 2014
Externally publishedYes
Event26th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2014 - Chicago, United States
Duration: Jun 29 2014Jul 3 2014

Bibliographical note

Funding Information:
Research supported by Chongqing University startup fund #0208001104411


  • Bijection
  • Generating function
  • Partition
  • Residue classes

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