International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2004 / Article

Open Access

Volume 2004 |Article ID 862780 |

Paul Hammond, Richard Lewis, "Congruences in ordered pairs of partitions", International Journal of Mathematics and Mathematical Sciences, vol. 2004, Article ID 862780, 4 pages, 2004.

Congruences in ordered pairs of partitions

Received28 Nov 2003
Revised12 Dec 2003


Dyson defined the rank of a partition (as the first part minus the number of parts) whilst investigating certain congruences in the sequence p1(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 p2(n).

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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