The Cranks for 5-Core Partitions

doi:10.3390/axioms1030372

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

Article

The Cranks for 5-Core Partitions

Louis Kolitsch

The University of Tennessee at Martin, Martin, TN 38238, USA

Received: 7 August 2012; in revised form: 21 September 2012 / Accepted: 26 November 2012 / Published: 3 December 2012

(This article belongs to the Special Issue q-Series and Related Topics in Special Functions and Analytic Number Theory)

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Abstract: It is well known that the number of 5-core partitions of 5^kn + 5^k − 1 is a multiple of 5^k. 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 5^kn + 5^k − 1 into 5^k classes of equal size.

Keywords: partitions; 5-cores; cranks

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MDPI and ACS Style

Kolitsch, L. The Cranks for 5-Core Partitions. Axioms 2012, 1, 372-383.

AMA Style

Kolitsch L. The Cranks for 5-Core Partitions. Axioms. 2012; 1(3):372-383.

Chicago/Turabian Style

Kolitsch, Louis. 2012. "The Cranks for 5-Core Partitions." Axioms 1, no. 3: 372-383.

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