Generate all partition's of a set and the set of equivalence relations

This is a bonus problem for the Algebra course at the UBB University

About the source code

To represent a partition, we will use a vector of integers, each integer representing the number of the subset in which the corresponding element is in

Partitioning -> Encoding

• {1, 2, 3} -> (1, 1, 1)
• {1} {2, 3} -> (2, 1, 1)
• {2} {1, 3} -> (1, 2, 1)
• {1, 2} {3} -> (2, 2, 1)
• {1} {2} {3} -> (3, 2, 1)

If we write the encodings backwards we obtain:

• 111
• 112
• 121
• 122
• 123

Be aware that the number 113 is missing because the encodings 112 and 113 translate to the same partitions

So, for a partition we just need to generate all the numbers with n-1 "digits" and the difference between the biggest two digits should be 1

If the number of elements of the set is to big(>10) we generate only the number of partitions of that set using Bell's triangle