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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 -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:
https://doi.org/10.1090/S0002-9939-04-07031-5

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