A systematic approach to matrix forms of the Pascal triangle: The twelve triangular matrix forms and relations

Abstract : This work initiates a systematic investigation into the matrix forms of the Pascal triangle as mathematical objects in their own right. The present paper is especially devoted to the so-called G-matrices, i.e. the set of the twelve (n+1)×(n+1) triangular matrix forms that can be derived from the Pascal triangle expanded to the level View the MathML source. For n=1, the G-matrix set reduces to a set of four distinct matrices. The twelve G-matrices are defined and the classic Pascal recursion is reformulated for each of the twelve G-matrices. Three sets of matrix transformations are then introduced to highlight different relations between the twelve G-matrices and for generating them from appropriately chosen subsets.
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European Journal of Combinatorics, Elsevier, 2010, 31 (5), pp.1205-1216. 〈10.1016/j.ejc.2009.10.009〉
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Soumis le : jeudi 16 juin 2011 - 11:34:02
Dernière modification le : jeudi 19 avril 2018 - 01:02:03

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Babiga Birregah, Prosper K. Doh, Kondo-Hloindo Adjallah. A systematic approach to matrix forms of the Pascal triangle: The twelve triangular matrix forms and relations. European Journal of Combinatorics, Elsevier, 2010, 31 (5), pp.1205-1216. 〈10.1016/j.ejc.2009.10.009〉. 〈inria-00600949〉

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