Apartition of a positive integer n is a sequence of integers (x1, . . xk) with x1 ≥ x2 ≥ xk ≥ 1 with x1 + · · · + xk = n. (note that the number of parts is not fixed here.) show that the number of partitions of n with at most k parts is the same as the number of partitions in which each part is of size at most k. you may want to do this by setting up a one-to-one function between the two kinds of partitions.