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The Absolute of the Comb Graph

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In the 1970s, R. Stanley introduced the comb graph 𝔼 whose vertices are indexed by the set of compositions of positive integers and branching reflects the ordering of compositions by inclusion. A. Vershik defined the absolute of a ℤ+-graded graph as the set of all ergodic probability central measures on it. We show that the absolute of 𝔼 is naturally parametrized by the space Ω = {(α1, α2, …) : αi ≥ 0, ∑iαi ≤ 1}.

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Authors and Affiliations

  1. St.Petersburg Department of Steklov Institute of Mathematics and St.Petersburg State University, St.Petersburg, Russia

    P. Nikitin

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  1. P. Nikitin
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Correspondence to P. Nikitin.

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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 481, 2019, pp. 125–135.

The work is supported by the RSF grant 17-71-20153.

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Nikitin, P. The Absolute of the Comb Graph. J Math Sci 247, 723–730 (2020). https://doi.org/10.1007/s10958-020-04834-w

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  • DOI: https://doi.org/10.1007/s10958-020-04834-w

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