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Egge, Loehr and Warrington gave in \cite{ELW} a combinatorial formula thatpermits to convert the expansion of a symmetric function, homogeneous of degree$n$, in terms of Gessel's fundamental quasisymmetric functions into anexpansion in terms of Schur functions. Surprisingly the Egge, Loehr andWarrington result may be shown to be simply equivalent to replacing the Gesselfundamental by a Schur function indexed by the same composition. In this paperwe give a direct proof of the validity of this replacement. This interpretationof the result in \cite{ELW} has already been successfully applied to Schurpositivity problems.

A note on passing from a quasi-symmetric function expansion to a Schur function expansion of a symmetric function