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A polynomial bound on solutions of quadratic equations in free groups

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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 solution sets of quadratic equations in a free group.

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Authors and Affiliations

  1. Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

    Igor G. Lysenok

  2. Department of Mathematical Sciences, Stevens Institute of Technology, Castle Point on Hudson, Hoboken, NJ, 07030-5991, USA

    Alexei G. Myasnikov

Authors
  1. Igor G. Lysenok
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  2. Alexei G. Myasnikov
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Correspondence to Igor G. Lysenok.

Additional information

Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2011, Vol. 274, pp. 148–190.

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Lysenok, I.G., Myasnikov, A.G. A polynomial bound on solutions of quadratic equations in free groups. Proc. Steklov Inst. Math. 274, 136–173 (2011). https://doi.org/10.1134/S0081543811060101

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  • DOI: https://doi.org/10.1134/S0081543811060101

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