Original scientific paper

https://doi.org/10.3336/gm.56.2.01

Limit theorems for numbers satisfying a class of triangular arrays

Igoris Belovas orcid.org/0000-0002-0478-1102 ; Institute of Data Science and Digital Technologies, Vilnius University, 04812 Vilnius, Lithuania

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Abstract

The paper extends the investigations of limit theorems for numbers satisfying a class of triangular arrays, defined by a bivariate linear recurrence with bivariate linear coefficients. We obtain the partial differential equation and special analytical expressions for the numbers using a semi-exponential generating function. We apply the results to prove the asymptotic normality of special classes of the numbers and specify the convergence rate to the limiting distribution. We demonstrate that the limiting distribution is not always Gaussian.

Keywords

Limit theorems, combinatorial numbers, partial difference equations, asymptotic enumeration, asymptotic normality

Hrčak ID:

267560

URI

https://hrcak.srce.hr/267560

Publication date:

23.12.2021.

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