ON THE MULTI-DIMENSIONAL PARTITIONS OF SMALL INTEGERS
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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 ≤ 14 and d ≥ 1 we derive a formula for the function P_d (n) where P_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.
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 ≤ 14 and d ≥ 1 we derive a formula for the function P_d (n) where P_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.
참고문헌 (7)
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