  The quon algebra is an approach to particle statistics in order to provide a
theory in which the Pauli exclusion principle and Bose statistics are violated
by a small amount. The quons are particles whose annihilation and creation
operators obey the quon algebra which interpolates between fermions and bosons.
In this paper we generalize these models by introducing a deformation of the
quon algebra generated by a collection of operators $a_{i,k}$, $(i,k) \in
\mathbb{N}^* \times [m]$, on an infinite dimensional vector space satisfying
the deformed $q$-mutator relations $a_{j,l} a_{i,k}^{\dag} = q a_{i,k}^{\dag}
a_{j,l} + q^{\beta_{-k,l}} \delta_{i,j}$. We prove the realizability of our
model by showing that, for suitable values of $q$, the vector space generated
by the particle states obtained by applying combinations of $a_{i,k}$'s and
$a_{i,k}^{\dag}$'s to a vacuum state $|0\rangle$ is a Hilbert space. The proof
particularly needs the investigation of the new statistic $\mathtt{cinv}$ and
representations of the colored permutation group.
