Summary: In this paper we will give a similar factorization as in [S. Meljanac and D. Svrtan, Math. Commun. 1, No. 1, 1–24 (1996; Zbl 0919.17010)], where certain matrix factorizations on Fock-like representation of a multiparametric quon algebra on the free associative algebra of noncommuting polynomials equipped with multiparametric partial derivatives are examined. In order to replace these matrix factorizations (given from the right) by twisted algebra computation, we first consider the natural action of the symmetric group \(S_n\) on the polynomial ring \(R_n\) in \(n^2\) commuting variables \(X_{a,b}\) and also introduce a twisted group algebra (defined by the action of \(S_n\) on \(R_n\)) which we denote by \(\mathcal{A}(S_n)\). Here we consider some factorizations given from the left because they will be more suitable in calculating the constants (= the elements which are annihilated by all multiparametric partial derivatives) in the free algebra of noncommuting polynomials.