A polynomial bound on solutions of quadratic equations in free groups
Igor Lysenok, Alexei Myasnikov
TL;DR
This paper establishes polynomial upper bounds on the size of shortest solutions to quadratic equations in free groups, improving understanding of solution complexity in algebraic structures.
Contribution
It introduces polynomial bounds for solutions of quadratic equations in free groups, including parametric solutions, advancing algebraic solution analysis.
Findings
Polynomial bounds on shortest solutions
Bounds apply to parametric solutions
Improved understanding of solution complexity
Abstract
We provide polynomial upper bounds on the size of a shortest solution for quadratic equations in a free group. A similar bound is given for parametric solutions in the description of solutions sets of quadratic equations in a free group.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Operator Algebra Research · Homotopy and Cohomology in Algebraic Topology