Hilbert series of right-angled affine Artin monoid $M(\widetilde{A}^{\infty}_{n})$

It is already proved that the growth rate of all the spherical Artin monoids is less than 4. In this paper, we find the Hilbert series of the associated right-angled affine Artin monoid M and also we discuss the recurrence relations and the growth of the monoid M .