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In the number theory of integer partitions, the numbers denote both the number of partitions of into exactly parts (that is, sums of positive integers that add to ), and the number of partitions of into parts of maximum size exactly . These two types of partition are in bijection with each other, by a diagonal reflection of their Young diagrams. Their numbers can be arranged into a triangle, the triangle of partition numbers, in which the th row gives the partition numbers :
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