#####
Séminaire Lotharingien de Combinatoire, B19b (1988).

[Formerly: Publ. I.R.M.A. Strasbourg, 1988, 361/S-19, p.
5-12.]

# Christian Choffrut

# A Remark on the Representation of the Free Partial Commutative Monoid

**Abstract.**
We consider free partially commutative monoids, i.e., free monoids
where some pairs of letters are allowed to commute. We show
that such a monoid can be faithfully represented by 2x2
matrices with integer entries if and only if iit is the direct
product of a free commutative monoid with a free product of
free commutative monoids.

The paper has been finally published under the title
"A remark on the representation of trace monoids" in
*Semigroup Forum* **40** (1990), 143-152.