On maximal chains of systems of word equations

We consider systems of word equations and their solution sets. We discuss some fascinating properties of those, namely the size of a maximal independent set of word equations, and proper chains of solution sets of those. We recall the basic results, extend some known results and formulate several fundamental problems of the topic.Comment: 10 pages. This is a journal article published in 2011, together with a note about a missing reference added in 201

Systems of word equations, polynomials and linear algebra: A new approach

We develop a new tool, namely polynomial and linear algebraic methods, for studying systems of word equations. We illustrate its usefulness by giving essentially simpler proofs of several hard problems. At the same time we prove extensions of these results. Finally, we obtain the first nontrivial upper bounds for the fundamental problem of the maximal size of independent systems. These bounds depend quadratically on the size of the shortest equation. No methods of having such bounds have been known before.Comment: 19 pages, submitted to a journal, extended version of the conference paper arXiv:1108.363