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 num...
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| Format: | Article |
| Language: | English |
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Vilnius University Press
2023-11-01
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| Series: | Lietuvos Matematikos Rinkinys |
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| Online Access: | https://www.journals.vu.lt/LMR/article/view/33577 |
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| _version_ | 1832593215002247168 |
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| author | Igoris Belovas |
| author_facet | Igoris Belovas |
| author_sort | Igoris Belovas |
| collection | DOAJ |
| description |
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.
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| format | Article |
| id | doaj-art-affc3b3403cb47b8b8b537c06bb09e6d |
| institution | Kabale University |
| issn | 0132-2818 2335-898X |
| language | English |
| publishDate | 2023-11-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Lietuvos Matematikos Rinkinys |
| spelling | doaj-art-affc3b3403cb47b8b8b537c06bb09e6d2025-01-20T18:15:02ZengVilnius University PressLietuvos Matematikos Rinkinys0132-28182335-898X2023-11-0164B10.15388/LMR.2023.33577Problems for combinatorial numbers satisfying a class of triangular arraysIgoris Belovas0Vilnius University 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. https://www.journals.vu.lt/LMR/article/view/33577combinatorial numberslimit theoremsasymptotic normality |
| spellingShingle | Igoris Belovas Problems for combinatorial numbers satisfying a class of triangular arrays Lietuvos Matematikos Rinkinys combinatorial numbers limit theorems asymptotic normality |
| title | Problems for combinatorial numbers satisfying a class of triangular arrays |
| title_full | Problems for combinatorial numbers satisfying a class of triangular arrays |
| title_fullStr | Problems for combinatorial numbers satisfying a class of triangular arrays |
| title_full_unstemmed | Problems for combinatorial numbers satisfying a class of triangular arrays |
| title_short | Problems for combinatorial numbers satisfying a class of triangular arrays |
| title_sort | problems for combinatorial numbers satisfying a class of triangular arrays |
| topic | combinatorial numbers limit theorems asymptotic normality |
| url | https://www.journals.vu.lt/LMR/article/view/33577 |
| work_keys_str_mv | AT igorisbelovas problemsforcombinatorialnumberssatisfyingaclassoftriangulararrays |