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On the asymptotic behaviour of the probability of existence of equivalent tuples with nontrivial structure in a random sequence
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V. G. Mikhailov
Published/Copyright:
December 9, 2008
Abstract
In a long enough sequence of discrete random variables, as a rule, an s-tuple exists of nontrivial structure, that is, a tuple with at least one repeated symbol. We consider the case where the sequence consists of n + s – 1 independent random variables taking the values 1, …, N with equal probabilities. It is shown that as n → ∞, ns3N–2 → 0 the probability of that in the sequence s-tuples exist with the same nontrivial structure is equal to 1 – (1 + n/N)se–sn/N (1 + o(1)).
Received: 2006-11-28
Revised: 2008-09-15
Published Online: 2008-12-09
Published in Print: 2008-December
© de Gruyter 2008
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Articles in the same Issue
- On stability of a vector combinatorial problem with MINMIN criteria
- On the asymptotic behaviour of the probability of existence of equivalent tuples with nontrivial structure in a random sequence
- Characteristics of random systems of linear equations over a finite field
- On the realisation of Boolean functions by informational graphs
- Estimates of the number of occurrences of vectors on cycles of linear recurring sequences over a finite field
- Finite generability of some groups of recursive permutations
- Independent systems of generators and the Hopf property for unary algebras
- Estimates of the complexity of approximation of continuous functions in some classes of determinate functions with delay
- On ranks, Green classes, and the theory of determinants of Boolean matrices
