Toward a polynomial basis of the algebra of peak quasisymmetric functions

Hazewinkel proved the Ditters conjecture that the algebra of quasisymmetric functions over the integers is free commutative by constructing a nice polynomial basis. In this paper, we prove a structure theorem for the algebra of peak quasisymmetric functions (PQSym) over the integers. It provides a polynomial basis of PQSym over the rational field, different from Hsiao’s basis, and implies the freeness of PQSym over its subring of symmetric functions spanned by Schur’s Q-functions.