The Number of Vector Partitions of n with the Crank m

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. 91-105.

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
• 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

References

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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 Swinnerton-Dyer, P. (1954), Some Properties of Partitions, Proc. London Math. Soc. 3(4): 84–106.