Question

Show that no. Of partitions of n is equal to the no. Of partitions of 2n with exactly n parts

Answer 1

Answer:

The number of partitions of n is equal to the # of the partitions of 2n divided into n parts. I know that the number of partitions of any integer ........................

Answer 2

Answer:

The number of partitions of any integer m into j parts equals the number of partitions of m with largest part j (easy bijective proof using Ferrer's diagrams). Thus the number of partitions of 2n into n parts equals the number of partitions of 2n with largest part n. The bijection between partitions of 2n with largest part n and partitions of n is straightforward.