Abstract
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 language | English (US) |
|---|---|
| Pages (from-to) | 289-295 |
| Number of pages | 7 |
| Journal | Discrete Mathematics and Theoretical Computer Science |
| State | Published - 2014 |
| Externally published | Yes |
| Event | 26th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2014 - Chicago, United States Duration: Jun 29 2014 → Jul 3 2014 |
Bibliographical note
Funding Information:Research supported by Chongqing University startup fund #0208001104411
Publisher Copyright:
© 2014 Discrete Mathematics and Theoretical Computer Science (DMTCS), Nancy, France
Keywords
- Bijection
- Generating function
- Partition
- Residue classes