Partition identities and geometric bijections

Pak, Igor

doi:10.1090/S0002-9939-04-07031-5

Partition identities and geometric bijections
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by Igor Pak PDF

Proc. Amer. Math. Soc. 132 (2004), 3457-3462 Request permission

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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