Affordable Access

Access to the full text

Generalized allocation scheme with cell occupancies from a fixed finite set

Authors
  • Timashev, Aleksandr N.1
  • 1 Institute of cryptography, communications and informatics, Russia , (Russia)
Type
Published Article
Journal
Discrete Mathematics and Applications
Publisher
De Gruyter
Publication Date
Oct 17, 2020
Volume
30
Issue
5
Pages
347–352
Identifiers
DOI: 10.1515/dma-2020-0031
Source
De Gruyter
Keywords
License
Yellow

Abstract

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 In(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.

Report this publication

Statistics

Seen <100 times