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

The Cranks for 5-Core Partitions

The University of Tennessee at Martin, Martin, TN 38238, USA
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 (CC BY 3.0).
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Kolitsch, L. The Cranks for 5-Core Partitions. Axioms 2012, 1, 372-383.

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