1 Answers
In the number theory of integer partitions, the numbers p k {\displaystyle p_{k}} denote both the number of partitions of n {\displaystyle n} into exactly k {\displaystyle k} parts , and the number of partitions of n {\displaystyle n} into parts of maximum size exactly k {\displaystyle k}. 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 n {\displaystyle n} th row gives the partition numbers p 1 , p 2 , … , p n {\displaystyle p_{1},p_{2},\dots ,p_{n}} :