Das, Sabuj and Mohajan, Haradhan (2014): The Number of Vector Partitions of n with the Crank m. Published in: International Journal of Reciprocal Symmetry and Theoretical Physics , Vol. 1, No. 2 (30 December 2014): pp. 91105.

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Abstract
This article shows how to find all vector partitions of any positive integral values of n, but only all vector partitions of 4, 5, and 6 are shown by algebraically. These must be satisfied by the definitions of crank of vector partitions.
Item Type:  MPRA Paper 

Original Title:  The Number of Vector Partitions of n with the Crank m 
English Title:  The Number of Vector Partitions of n with the Crank m 
Language:  English 
Keywords:  Vector partitions, Crank, Congruences, Modulo 
Subjects:  C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models ; Multiple Variables C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling 
Item ID:  83697 
Depositing User:  Haradhan Kumar Mohajan 
Date Deposited:  09 Jan 2018 05:11 
Last Modified:  21 Oct 2019 13:55 
References:  Andrews G.E. (1985), The Theory of Partitions, Encyclopedia of Mathematics and its Application, vol. 2 (Gc, Rotaed) AddisonWesley, Reading, mass, 1976 (Reissued, Cambridge University, Press, London and New York 1985). Andrews G.E. and Garvan F.G. (1988), Dyson’s Crank of a Partition, Bulletin (New series) of the American Mathematical Society, 18(2): 167–171. Atkin, A.O.L. and SwinnertonDyer, P. (1954), Some Properties of Partitions, Proc. London Math. Soc. 3(4): 84–106. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/83697 