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A systematic approach to matrix forms of the Pascal triangle: The twelve triangular matrix forms and relations
- Source :
-
European Journal of Combinatorics . Jul2010, Vol. 31 Issue 5, p1205-1216. 12p. - Publication Year :
- 2010
-
Abstract
- 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 triangular matrix forms that can be derived from the Pascal triangle expanded to the level . For , 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. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 01956698
- Volume :
- 31
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- European Journal of Combinatorics
- Publication Type :
- Academic Journal
- Accession number :
- 50394954
- Full Text :
- https://doi.org/10.1016/j.ejc.2009.10.009