Let N be any integer. Consider the collection of all partitions of N, Is there anything related has been studied? If not ? can we create some kind of Graphs?
The number of all partitions is equal to 2^(N-1) since the order of addends is important. For pedagogical aspect of the problem you can see publication in CERME 3 materials: I. Sinitsky. PRE-ALGEBRA COMBINATORIAL PROBLEMS AND ALGORITHMS IN PRIMARY SCHOOL MATHEMATICS (Thematic group 6 materials)