${\displaystyle (x+x^2+x^3+x^4{)}^2=x^2(1+x{)}^2(1+x^2{)}^2=[x+2x^2+x^3][x+2x^3+x^5].}$

corresponds to the re-labelling 1, 2, 2, 3 and 1, 3, 3, 5 .