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In number theory and combinatorics, a partition of a positive integer ''n'', also called an integer partition, is a way of writing ''n'' as a sum of positive integers. Two sums that differ only in the order of their summands are considered the same partition. (If order matters, the sum becomes a composition.) For example, 4 can be partitioned in five distinct ways: :4 :3 + 1 :2 + 2 :2 + 1 + 1 :1 + 1 + 1 + 1 The order-dependent composition 1 + 3 is the same partition as 3 + 1, while 1 + 2 + 1 and 1 + 1 + 2 are the same partition as 2 + 1 + 1. A summand in a partition is also called a part. The number of partitions of ''n'' is given by the partition function ''p''(''n''). So ''p''(4) = 5. The notation ''λ'' (unicode:⊢) ''n'' means that ''λ'' is a partition of ''n''. Partitions can be graphically visualized with Young diagrams or Ferrers diagrams. They occur in a number of branches of mathematics and physics, including the study of symmetric polynomials, the symmetric group and in group representation theory in general. ==Examples== The seven partitions of 5 are: * 5 * 4 + 1 * 3 + 2 * 3 + 1 + 1 * 2 + 2 + 1 * 2 + 1 + 1 + 1 * 1 + 1 + 1 + 1 + 1 In some sources partitions are treated as the sequence of summands, rather than as an expression with plus signs. For example, the partition 2 + 2 + 1 might instead be written as the tuple or in the even more compact form where the superscript indicates the number of repetitions of a term. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Partition (number theory)」の詳細全文を読む スポンサード リンク
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