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Congruences in ordered pairs of partitions

journal contribution
posted on 2023-06-08, 13:47 authored by Paul Hammond, Richard Lewis
Dyson defined the rank of a partition (as the first part minus the number of parts) whilst investigating certain congruences in the sequence p-1(n). The rank has been widely studied as have been other statistics, such as the crank. In this paper a “birank” is defined which relates to ordered pairs of partitions, and is used in an elementary proof of a congruence in p-2(n)

History

Publication status

  • Published

Journal

International Journal of Mathematics and Mathematical Sciences

ISSN

0161-1712

Publisher

Hindawi Publishing Corporation

Issue

47

Volume

2004

Page range

2509-2512

Department affiliated with

  • Mathematics Publications

Notes

The interested reader might also like to look at Frank Garvan's "Biranks for partitions into 2 colors" http://arxiv.org/pdf/0909.4892.pdf and http://www.math.ufl.edu/~fgarvan/papers/birank.pdf

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2012-11-19

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