  We study the Gnedin-Kingman graph, which corresponds to Pieri's rule for the
monomial basis $\{M_{\lambda}\}$ in the algebra $\mathrm{QSym}$ of
quasisymmetric functions. The paper contains a detailed announcement of results
concerning the classification of indecomposable semifinite harmonic functions
on the Gnedin-Kingman graph. For these functions, we also establish a
multiplicativity property, which is an analog of the Vershik-Kerov ring
theorem.
