Séminaire Lotharingien de Combinatoire, B19b (1988).
[Formerly: Publ. I.R.M.A. Strasbourg, 1988, 361/S-19, p.
A Remark on the Representation of the Free Partial Commutative Monoid
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.