Geodesic
Semifinite harmonic functions on the Gnedin--Kingman graph
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXI, Tome 498 (2020), pp. 38-54

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We study the Gnedin–Kingman graph, which corresponds to the Pieri 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. 
@article{ZNSL_2020_498_a3,
     author = {N. A. Safonkin},
     title = {Semifinite harmonic functions on the {Gnedin--Kingman} graph},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {38--54},
     publisher = {mathdoc},
     volume = {498},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_498_a3/}
}
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N. A. Safonkin. Semifinite harmonic functions on the Gnedin--Kingman graph. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXI, Tome 498 (2020), pp. 38-54. http://geodesic.mathdoc.fr/item/ZNSL_2020_498_a3/