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The number of partitions of the integer $ N$ into $ M$ nonzero positive integers

Author: W. J. A. Colman
Journal: Math. Comp. 39 (1982), 213-224
MSC: Primary 10A45
MathSciNet review: 658226
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Abstract: The function $ {p_m}(n)$ is defined as the number of partitions of the integer n into exactly m nonzero positive integers where the order is irrelevant.

A series in which the leading terms alternate in sign is given for $ {p_m}(n)$ which yields good numerical estimates.

References [Enhancements On Off] (What's this?)

  • [1] George E. Andrews, The theory of partitions, Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1976. Encyclopedia of Mathematics and its Applications, Vol. 2. MR 0557013
  • [2] L. E. Dickson, History of the Theory of Numbers, Vol. 2, Chelsea, New York, 1966.
  • [3] H. Gupta, Tables of Partitions, The Royal Society Mathematical Tables, Vol. 4, Cambridge, 1958.
  • [4] G. J. Rieger, Über Partitionen, Math. Ann. 138 (1959), 356–362 (German). MR 0108472

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Article copyright: © Copyright 1982 American Mathematical Society