  In this paper we will give a similar factorization as in \cite{4}, \cite{5},
where the autors Svrtan and Meljanac examined certain matrix factorizations on
Fock-like representation of a multiparametric quon algebra on the free
associative algebra of noncommuting polynomials equiped with multiparametric
partial derivatives. 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.
