1 + 3 and 3 + 1 are the same partition of 4, because it's a sum with the same two numbers. The order of the 1 and the 3 doesn't matter for partitions.

But that's two compositions.

I think this article could really use more applied, concrete examples if it's intended for programmers.

It seems their idea for connecting math and programming was printing out a bunch of C code, without further motivation. But coding is an applied field, developpers will want a concrete idea of what they can do with it.

This is still too abstract.