East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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ON THE MULTI-DIMENSIONAL PARTITIONS OF SMALL INTEGERS

  • Kim, Jun-Kyo (Department of Mathematics, Pusan National University)
  • Received : 2011.05.03
  • Accepted : 2011.12.16
  • Published : 2012.01.31
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Abstract

For each dimension exceeds 1, determining the number of multi-dimensional partitions of a positive integer is an open question in combinatorial number theory. For n ${\leq}$ 14 and d ${\geq}$ 1 we derive a formula for the function ${\wp}_d(n)$ where ${\wp}_d(n)$ denotes the number of partitions of n arranged on a d-dimensional space. We also give an another definition of the d-dimensional partitions using the union of finite number of divisor sets of integers.

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References

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