Method for constructing bijections for classical partition identities.

@article{Garsia1981MethodFC,
  title={Method for constructing bijections for classical partition identities.},
  author={Adriano M. Garsia and Stephen C. Milne},
  journal={Proceedings of the National Academy of Sciences of the United States of America},
  year={1981},
  volume={78 4},
  pages={2026-8}
}
We sketch the construction of a bijection between the partitions of n with parts congruent to 1 or 4 (mod 5) and the partitions of n with parts differing by at least 2. This bijection is obtained by a cut-and-paste procedure that starts with a partition in one class and ends with a partition in the other class. The whole construction is a combination of a bijection discovered quite early by Schur and two bijections of our own. A basic principle concerning pairs of involutions provides the key… CONTINUE READING

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