Next Article in Journal
On the Equilibria of Generalized Dynamical Systems
Next Article in Special Issue
Generating Functions for q-Apostol Type Frobenius–Euler Numbers and Polynomials
Previous Article in Journal / Special Issue
New Curious Bilateral q-Series Identities
Axioms 2012, 1(3), 372-383; doi:10.3390/axioms1030372

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
View Full-Text   |   Download PDF [288 KB, uploaded 3 December 2012]


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) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Share & Cite This Article

Further Mendeley | CiteULike
Export to BibTeX |
EndNote |
MDPI and ACS Style

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

View more citation formats

Related Articles

Article Metrics


[Return to top]
Axioms EISSN 2075-1680 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert