I will show that as we pass from n to n+1, The basis of the quotient for n is included in the quotient for n+1. In fact I show several potential inclusion that has consequences on the structure of the Hilbert series of the quotient. I will also recall that when we have free Hopf algebra we can determine the infinite Hilbert series. I will do so for quotient of r-QSym/s-QSym. That last part was inspired by talks during A. Lauve's visit.