Problems for combinatorial numbers satisfying a class of triangular arrays

Numbers satisfying a class of triangular arrays, defined by a bivariate first-order linear difference equation with linear coefficients, include a wide range of combinatorial numbers: binomial coefficients, Morgan numbers, Stirling numbers of the first and the second types, non-central Stirling numb...

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Bibliographic Details
Published inLietuvos matematikos rinkinys Vol. 64; no. B; pp. 16 - 22
Main Author Belovas, Igoris
Format Journal Article
LanguageEnglish
Published Vilniaus universiteto leidykla / Vilnius University Press 20.11.2023
Vilnius University Press
Subjects
asymptotic normality
combinatorial numbers
limit theorems
asymptotic normality
asimptotinis normalumas
ribinės teoremos
combinatorial numbers
limit theorems
kombinatoriniai skaičiai
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ISSN0132-2818
2335-898X
DOI10.15388/LMR.2023.33577

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Summary:Numbers satisfying a class of triangular arrays, defined by a bivariate first-order linear difference equation with linear coefficients, include a wide range of combinatorial numbers: binomial coefficients, Morgan numbers, Stirling numbers of the first and the second types, non-central Stirling numbers, Eulerian numbers, Lah numbers, and their generalizations. In this work, we derive the general analytic expression of the numbers satisfying a class of triangular arrays and propose problems (both teaching and unsolved ones) for undergraduates studying probability theory and analytical combinatorics subjects in the study programs of the fields of mathematics and computer science. Some of the unsolved challenges can also be used as the basis for a thesis.
ISSN:0132-2818
2335-898X
DOI:10.15388/LMR.2023.33577