Systems of Word Equations and Polynomials: a New Approach
  We develop new polynomial methods for studying systems of word equations. We use them to improve some earlier results and to analyze how sizes of systems of word equations satisfying certain independence properties depend on the lengths of the equations. These methods give the first nontrivial upper bounds for the sizes of the systems. 
Aleksi Saarela (Turku Centre for Computer Science TUCS and Department   of Mathematics, University of Turku)
cs.FL