Author(s):
Cruz, Carla 
; Falcão, M. I. ; Malonek, H. R.
Date: 2013
Persistent ID: http://hdl.handle.net/1822/29180
Origin: RepositóriUM - Universidade do Minho
Subject(s): Pascal's tetrahedron; Clifford Analysis
Document details
About Pascal’s tetrahedron with hypercomplex entries
Description
"11th International Conference of Numerical Analysis and Applied Mathematics, 21 - 27 September 2013" It is evident, that the properties of monogenic polynomials in $(n+1)-$real variables significantly depend on the generators $e_1, e_2, \dots, e_n$ of the underlying $2^n$-dimensional Clifford algebra $Cl_{0,n}$ over $\mathbb{R}$ and their interactions under multiplication. The case of $n=3$ is studied through the consideration of Pascal's tetrahedron with hypercomplex entries as special case of the general Pascal simplex for arbitrary $n$, which represents a useful geometric arrangement of all possible products. The different layers ${\mathcal{L}_k$ of Pascal's tetrahedron (or pyramid) are built by ordered symmetric products contained in the trinomial expansion of $(e_1+e_2+e_3)^k$, $k=0,1,\dots$.
"11th International Conference of Numerical Analysis and Applied Mathematics, 21 - 27 September 2013" It is evident, that the properties of monogenic polynomials in $(n+1)-$real variables significantly depend on the generators $e_1, e_2, \dots, e_n$ of the underlying $2^n$-dimensional Clifford algebra $Cl_{0,n}$ over $\mathbb{R}$ and their interactions under multiplication. The case of $n=3$ is studied through the consideration of Pascal's tetrahedron with hypercomplex entries as special case of the general Pascal simplex for arbitrary $n$, which represents a useful geometric arrangement of all possible products. The different layers ${\mathcal{L}_k$ of Pascal's tetrahedron (or pyramid) are built by ordered symmetric products contained in the trinomial expansion of $(e_1+e_2+e_3)^k$, $k=0,1,\dots$.
Document Type
Conference Object
Language English
Language English
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