Semifinite harmonic functions on the Gnedin-Kingman graph

We study the Gnedin-Kingman graph, which corresponds to Pieri's rule for the monomial basis $\{M_λ\}$ 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.

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