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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Partition identities and geometric bijections


Author: Igor Pak
Journal: Proc. Amer. Math. Soc. 132 (2004), 3457-3462
MSC (2000): Primary 05A17; Secondary 05A15, 05A19, 11P81
Published electronically: July 14, 2004
MathSciNet review: 2084064
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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.


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Additional Information

Igor Pak
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07031-5
PII: S 0002-9939(04)07031-5
Keywords: Partition identities, bijections, simple cones
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
Article copyright: © Copyright 2004 American Mathematical Society