Full Article: PDF
Scientific Object Identifier: http://s-o-i.org/1.1/TAS-03-107-56
DOI: https://dx.doi.org/10.15863/TAS.2022.03.107.56
Language: Russian
Citation: Okbaeva, N. (2022). Pascal's triangle, its planar and spatial generalizations. ISJ Theoretical & Applied Science, 03 (107), 815-823. Soi: http://s-o-i.org/1.1/TAS-03-107-56 Doi: https://dx.doi.org/10.15863/TAS.2022.03.107.56 |
Pages: 815-823
Published: 30.03.2022
Abstract: This article discusses historical information about the appearance of Pascal's triangle and binomial coefficients, and their new properties obtained by mathematicians in the last 40 years (forty years). Generalized Pascal triangles of the s-th order, Pascal's pyramid and hyperpyramids, as well as Fibonacci, Luke, Catalan triangles, etc. are studied. Generalized binomial coefficients of the s-th order, polynomial coefficients and other analogues of binomial coefficients are considered. [18]
Key words: Pascal's triangles, binomial coefficients, generalized binomial coefficients of the s-th order, trinomial coefficients, polynomial coefficients.
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