Two Kinds Of Partitions

Discrete Mathematics Level 3

Let p(n) p(n) be the number of partitions of n n. Let q(n)q(n) be the number of partitions of 2n 2n into exactly nn parts. For example, q(3)=3q(3) = 3 because 6=4+1+1=3+2+1=2+2+2. 6 = 4+1+1 = 3+2+1 = 2+2+2. Compute p(12)−q(12). p(12)-q(12).

Definition: A partition of an integer is an expression of the integer as a sum of one or more positive integers, called parts. Two expressions consisting of the same parts written in a different order are considered the same partition ("order does not matter").

Patrick Corn by Patrick Corn
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