On Systems of Equations over Free Partially Commutative Groups

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Version 2: Corrected Section 3.3: instead of lexicographical normal forms we now use a normal form due to V. Diekert and A. Muscholl. Consequent changes made and some misprints corrected. Using an analogue of Makanin-Razborov diagrams, we give an effective description of the solution set of systems of equations over a partially commutative group (right-angled Artin group) G. Equivalently, we give a parametrisation of Hom(H, G), where H is a finitely generated group.