I have a question related with number of additive partition or method similar like this: $p(5)=1+4=2+3=1+1+1+1+1=1+1+1+2=1+2+2=1+1+3$
For a given number $n$,if we are trying to calculate number of additive partition of $p(n\cdot k)$ where $k$ is some integer,or $p(n+a+c)$ , $a,c \in \mathbb Z$, is there commutative rules or something similar to calculate number of partition of sum of some numbers?or number of partition of some number multiplied by another number? For example like this $p(n+k)\overset{?}{=}p(n)+p(k)?$
Please help me