ON THE MULTI-DIMENSIONAL PARTITIONS OF SMALL INTEGERS

• Journal title : East Asian mathematical journal
• Volume 28, Issue 1,  2012, pp.101-107
• Publisher : Youngnam Mathematical Society
• DOI : 10.7858/eamj.2012.28.1.101
Title & Authors
ON THE MULTI-DIMENSIONAL PARTITIONS OF SMALL INTEGERS
Kim, Jun-Kyo;

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 $\small{{\leq}}$ 14 and d $\small{{\geq}}$ 1 we derive a formula for the function $\small{{\wp}_d(n)}$ where $\small{{\wp}_d(n)}$ 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.
Keywords
partitions of integers;multidimensional partition;combinatorial number theory;additive number theory;
Language
English
Cited by
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