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...
| Published in: | Lietuvos Matematikos Rinkinys |
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| Format: | Article |
| Language: | English |
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Vilnius University Press
2023-11-01
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| Online Access: | https://www.journals.vu.lt/LMR/article/view/33577 |
| 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.
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| ISSN: | 0132-2818 2335-898X |