conjugate partition
Quick Summary
In mathematics, a conjugate partition is derived from a given partition of an integer. A partition of an integer n is the number of ways n can be expressed as a sum of smaller positive integers. For example, the integer 7 can be partitioned in several ways, such as 5 + 1 + 1, 4 + 2 + 1, 3 + 3 + 1, and 3 + 2 + 2.1
A conjugate partition is found by using a Ferrers diagram, which visually represents a partition. By rotating this diagram, one can obtain the conjugate partition. A key property is that the number of partitions of n into k parts equals the number of partitions of n where k is the largest part.2
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