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Zap. Nauchn. Sem. POMI, 2018, Volume 468, Pages 58–74 (Mi znsl6586)  

I

The boundary of the refined Kingman graph

M. V. Karev, P. P. Nikitin

St. Petersburg Department of Steklov Institute of Mathematics, St. Petersburg, Russia

Abstract: We introduce the refined Kingman graph $\mathbb D$ whose vertices are indexed by the set of compositions of positive integers and multiplicity function reflects the Pieri rule for quasisymmetric monomial functions. We show that the Martin boundary of $\mathbb D$ can be identified with the space $\Omega$ of all sets of disjoint open subintervals of $[0,1]$ and coincides with the minimal boundary of $\mathbb D$.

Key words and phrases: Kingman graph, refined Kingman graph, quasisymmetric monomial functions, Martin boundary, ergodic central measures, absolute.

Funding Agency Grant Number
Russian Science Foundation 17-71-20153
Supported by the RSF grant 17-71-20153.


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English version:
Journal of Mathematical Sciences (New York), 2019, 240:5, 539–550

UDC: 519.217.72+517.987
Received: 23.08.2018
Language:

Citation: M. V. Karev, P. P. Nikitin, “The boundary of the refined Kingman graph”, Representation theory, dynamical systems, combinatorial methods. Part XXIX, Zap. Nauchn. Sem. POMI, 468, POMI, St. Petersburg, 2018, 58–74; J. Math. Sci. (N. Y.), 240:5 (2019), 539–550

Citation in format AMSBIB
\Bibitem{KarNik18}
\by M.~V.~Karev, P.~P.~Nikitin
\paper The boundary of the refined Kingman graph
\inbook Representation theory, dynamical systems, combinatorial methods. Part~XXIX
\serial Zap. Nauchn. Sem. POMI
\yr 2018
\vol 468
\pages 58--74
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6586}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2019
\vol 240
\issue 5
\pages 539--550
\crossref{https://doi.org/10.1007/s10958-019-04372-0}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85068229451}


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