Geodesic
The Equivalence between the Schur Order and the Stochastic Orders Generated by the Scheme of Allocation of Particles into Cells
Matematičeskie zametki, Tome 93 (2013) no. 1, pp. 56-62

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In 1982, it was proved that the Schur partial-order relation on the set of distributions on $\{1,2,\dots\}$ is equivalent to the order relation generated the number of nonempty cell distributions by the scheme of independent allocation of particles into cells. Here it is shown that the same partial-order relation is generated by distributions of numbers of cells occupied by at least $r$ particles for any $r\ge 2$.
Keywords: allocation of particles into cells, Schur partial-order relation, stochastic order
Mots-clés : multinomial distribution. 
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A. M. Zubkov; T. A. Tatarenko. The Equivalence between the Schur Order and the Stochastic Orders Generated by the Scheme of Allocation of Particles into Cells. Matematičeskie zametki, Tome 93 (2013) no. 1, pp. 56-62. http://geodesic.mathdoc.fr/item/MZM_2013_93_1_a4/