Generalized allocation scheme with cell occupancies from a fixed finite set
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Aleksandr N. Timashev
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.
Originally published in Diskretnaya Matematika (2019) 31, №1, 125–132 (in Russian).
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- Post theorem for strongly dependent n-ary semigroups
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Articles in the same Issue
- Attribute-efficient learning of Boolean functions from Post closed classes
- Easily testable circuits in Zhegalkin basis in the case of constant faults of type “1” at gate outputs
- Post theorem for strongly dependent n-ary semigroups
- Effective parallelization strategy for the solution of subset sum problems by the branch-and-bound method
- On the number of ones in outcome sequence of extended Pohl generator
- The number of sumsets in Abelian group
- Generalized allocation scheme with cell occupancies from a fixed finite set
- Universal functions for linear functions depending on two variables
