A non-commutative \(n\)-nomial formula (Q2478041)

In this paper the author gives a general \(n\)-nomial expansion formula for \((x_1+\cdots+ x_n)^m\) in terms of degree \(m\) monomials in \(x_1,\dots, x_n\), under the assumption \(x_j x_i= p_{ij} x_i x_j\) for \(1\leq i< j\leq n\). This is a generalization of an early result independently given by \textit{M. P. Schützenberger} [C. R. Acad. Sci., Paris 236, 352--353 (1953; Zbl 0051.09401)].