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The Number of Vector Partitions of n (Counted According to the Weight) with the Crank m
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.
Vector Partitions, Crank, Congruences, Modulo.
- Andrews G.E. (1985), The Theory of Partitions, Encyclopedia of Mathematics and its Application, vol. 2 (G-c, Rotaed) Addison-Wesley, 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 Swinnerton-Dyer, P. (1954), Some Properties of Partitions, Proc. London Math. Soc. 3(4): 84–106.
- Das S. 2014. Congruence Properties of Andrews’ SPT- Function ABC Journal of Advanced Research, 3, 47-56.
- Mohajan HK. Upper Limit of the Age of the Universe with Cosmological Constant International Journal of Reciprocal Symmetry and Theoretical Physics. 2014;1(1):43-68.
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