Duboc C. (1986) Equations in free partially commutative monoids. In: Monien B., Vidal-Naquet G. (eds) STACS 86. STACS 1986. Lecture Notes in Computer Science, vol 210. Springer, Berlin, Heidelberg
We characterize the solutions of all the equations in two unknowns in the free partially commutative monolds. We show that the solutions are basically cyclic. Afterwards, we define the transposition (t and t′ are transposed iff t=xy and t′=yx) and the conjugacy relations (t and t′ are conjugate iff tλ=λt′). We show that the conjugacy is the transitive closure of the transposition and that the set of conjugacy factors λ is a recognizable subset of the partially commutative monoid.