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The equivalence between the Schur order and the stochastic orders generated by the scheme of allocation of particles into cells

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Abstract

In 1982, it was proved that the Schur partial-order relation on the set of distributions on {1, 2, ...} is equivalent to the order relation generated by the number of nonempty cell distributions in the scheme of independent allocation of particles into cells. Here it is shown that the same partialorder relation is generated by distributions of numbers of cells occupied by at least r particles for any r ≥ 2.

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References

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Authors and Affiliations

  1. Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia

    A. M. Zubkov

  2. Moscow State University, Moscow, Russia

    T. A. Tatarenko

Authors
  1. A. M. Zubkov
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  2. T. A. Tatarenko
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Correspondence to A. M. Zubkov.

Additional information

Original Russian Text © A. M. Zubkov, T. A. Tatarenko, 2013, published in Matematicheskie Zametki, 2013, Vol. 93, No. 1, pp. 56–62.

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Zubkov, A.M., Tatarenko, T.A. The equivalence between the Schur order and the stochastic orders generated by the scheme of allocation of particles into cells. Math Notes 93, 69–74 (2013). https://doi.org/10.1134/S0001434613010070

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  • DOI: https://doi.org/10.1134/S0001434613010070

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