About Pascal'S Tetrahedron With Hypercomplex Entries

It is evident, that the properties of monogenic polynomials in (n + 1)-real variables significantly depend on the generators e(1), e(2), ... , e(n) of the underlying 2(n)-dimensional Clifford algebra Cl-0,Cl-n over 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 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, ... .