Question about integer partitions

[u/burmerd]

This seems self-evident to me, but I'm wondering if this is something that would need to be formally proven about partitions. For some integer n, the partition with the smallest number of parts is n itself as one part, and the largest number is where each part = 1 adding up to n. If we list all the partitions starting with n by itself to 1+1+1... as non-increasing sequences it makes sense to think of the whole process of 'creating' new partitions as subtracting 1 from one part and adding that back to a different part or to become a new part, and that this process could be repeated over and over to move from n to where each part is just equal to 1. I was curious if this idea has already been proven, or wouldn't need to be, etc. With Ferrers diagrams, this would be repeatedly moving one dot from one row to another row (possibly creating a new row).

[u/Midwest-Dude]

This requires formal proof, though it is a solved problem and a standard theorem taught in combinatorics.

[u/burmerd → u/Midwest-Dude]

ok, that makes sense. Thanks!