Author(s): Cruz, Carla ; Falcão, M.Irene ; Malonek, Helmuth R. ; Tomaz, Graça
Date: 2026
Persistent ID: http://hdl.handle.net/10314/10288
Origin: Repositório Científico da Universidade Politécnica da Guarda
Subject(s): Pascal n-simplex; Clifford algebra; generalized multinomial formula
We propose a generalization of the Pascal n-simplex by considering the generators e_1, e_2,..., e_n of the 2^n−dimensional Clifford algebra C_{0,n} over R in the multinomial expansion of powers of their sum. We investigate various patterns within this structure and examine several of its properties and associated combinatorial identities. Our results establish a direct connection between this hypercomplex Pascal n-simplex and the terms of a generalized Vietoris number sequence, which plays an important role in the theory of Appell hypercomplex polynomials.
