Compositions and partitions

Concepts

• Integer composition 10 exercisesA composition of a positive integer n is a way of writing it as an ordered sum of positive integers, where the order of the summa…
• Integer partition 10 exercisesA partition of an integer n is a way of writing n as a sum of positive integers, where the order of the summands does not matter.…
• Partition generating function 10 exercisesThe partition generating function is the formal series ∑_n≥ 0 p(n) x^n, where p(n) counts the partitions of the integer n.
• Pentagonal number theorem 10 exercisesEuler's pentagonal number theorem states that the product prod_n≥1(1-x^n) equals an alternating sum of powers of x indexed by gen…