commutive polyomials ? A(B) = B(A) ??

[bo198214]

I think I don't understand the question, say I take \(A=x^3\), \(B=x^9\) and \(C = x^{27}\)
then \(A\circ B = B\circ A = x^{27}\), \(A\circ C = C\circ A = x^{81}\) and \(B\circ C = C\circ B = x^{243}\).
You can take any initial polynomial A and just set \(B=A^{\circ m}\) and \(C=A^{\circ n}\) for some odd m,n ...