Glasnik Matematicki, Vol. 56, No. 2 (2021), 195-223. \( \)

LIMIT THEOREMS FOR NUMBERS SATISFYING A CLASS OF TRIANGULAR ARRAYS

Igoris Belovas

Institute of Data Science and Digital Technologies, Vilnius University, 04812 Vilnius, Lithuania
e-mail:Igoris.Belovas@mif.vu.lt

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.

2020 Mathematics Subject Classification.   05A15, 05A16, 39A06, 39A14, 60F05

Key words and phrases.   Limit theorems, combinatorial numbers, partial difference equations, asymptotic enumeration, asymptotic normality

Full text (PDF) (access from subscribing institutions only)

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

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