Partition identities and geometric bijections
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Abstract:
We present a geometric framework for a class of partition identities. We show that there exists a unique bijection proving these identities, which satisfies certain linearity conditions. In particular, we show that Corteel’s bijection enumerating partitions with nonnegative $r$-th differences can be obtained by our approach. Other examples and generalizations are presented.References
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Additional Information
- Igor Pak
- Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
- MR Author ID: 293184
- ORCID: 0000-0001-8579-7239
- Received by editor(s): July 24, 2002
- Received by editor(s) in revised form: August 30, 2002
- Published electronically: July 14, 2004
- Communicated by: John R. Stembridge
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 3457-3462
- MSC (2000): Primary 05A17; Secondary 05A15, 05A19, 11P81
- DOI: https://doi.org/10.1090/S0002-9939-04-07031-5
- MathSciNet review: 2084064