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Axioms 2012, 1(3), 372-383; doi:10.3390/axioms1030372
Article

The Cranks for 5-Core Partitions

Received: 7 August 2012 / Revised: 21 September 2012 / Accepted: 26 November 2012 / Published: 3 December 2012
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Abstract

It is well known that the number of 5-core partitions of 5kn + 5k − 1 is a multiple of 5k. In [1] a statistic called a crank was developed to sort the 5-core partitions of 5n + 4 and 25n + 24 into 5 and 25 classes of equal size, respectively. In this paper we will develop the cranks that can be used to sort the 5-core partitions of 5kn + 5k − 1 into 5k classes of equal size.
Keywords: partitions; 5-cores; cranks partitions; 5-cores; cranks
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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Kolitsch, L. The Cranks for 5-Core Partitions. Axioms 2012, 1, 372-383.

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