Geodesic
Generalized allocation scheme with cell occupancies from a fixed finite set
Diskretnaya Matematika, Tome 31 (2019) no. 1, pp. 125-132

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider a generalized scheme of allocation of $n$ particles (elements) over unordered cells (components) under the condition that the number of particles in each cell belongs to a fixed finite set $A$ of positive integers. A new asymptotic estimates for the total number $I_n(A)$ of variants of allocations of $n$ particles are obtained under some conditions on the set $A$; these estimates have an explicit form (up to equivalence). Some examples of combinatorial-probabilistic character are given to illustrate by particular cases the notions introduced and results obtained. For previously known theorems on the convergence to the normal law of the total number of components and numbers of components with given cardinalities the norming parameters are obtained in the explicit form without using roots of algebraic or transcendent equations.
Keywords: generalized allocation scheme, cell contents, finite set, asymptotic normality. 
@article{DM_2019_31_1_a7,
     author = {A. N. Timashev},
     title = {Generalized allocation scheme with cell occupancies from a fixed finite set},
     journal = {Diskretnaya Matematika},
     pages = {125--132},
     publisher = {mathdoc},
     volume = {31},
     number = {1},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2019_31_1_a7/}
}
TY  - JOUR
AU  - A. N. Timashev
TI  - Generalized allocation scheme with cell occupancies from a fixed finite set
JO  - Diskretnaya Matematika
PY  - 2019
SP  - 125
EP  - 132
VL  - 31
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2019_31_1_a7/
LA  - ru
ID  - DM_2019_31_1_a7
ER  - 
%0 Journal Article
%A A. N. Timashev
%T Generalized allocation scheme with cell occupancies from a fixed finite set
%J Diskretnaya Matematika
%D 2019
%P 125-132
%V 31
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2019_31_1_a7/
%G ru
%F DM_2019_31_1_a7
A. N. Timashev. Generalized allocation scheme with cell occupancies from a fixed finite set. Diskretnaya Matematika, Tome 31 (2019) no. 1, pp. 125-132. http://geodesic.mathdoc.fr/item/DM_2019_31_1_a7/