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 Tr. Mat. Inst. Steklova, 2011, Volume 274, Pages 148–190 (Mi tm3318)

A polynomial bound on solutions of quadratic equations in free groups

Igor G. Lysenoka, Alexei G. Myasnikovb

a Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia
b Department of Mathematical Sciences, Stevens Institute of Technology, Castle Point on Hudson, Hoboken, NJ, USA

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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English version:
Proceedings of the Steklov Institute of Mathematics, 2011, 274, 136–173

Bibliographic databases:

Document Type: Article
UDC: 512.54.05+510.52

Citation: Igor G. Lysenok, Alexei G. Myasnikov, “A polynomial bound on solutions of quadratic equations in free groups”, Algorithmic aspects of algebra and logic, Collected papers. Dedicated to Academician Sergei Ivanovich Adian on the occasion of his 80th birthday, Tr. Mat. Inst. Steklova, 274, MAIK Nauka/Interperiodica, Moscow, 2011, 148–190; Proc. Steklov Inst. Math., 274 (2011), 136–173

Citation in format AMSBIB
\Bibitem{LysMya11} \by Igor~G.~Lysenok, Alexei~G.~Myasnikov \paper A polynomial bound on solutions of quadratic equations in free groups \inbook Algorithmic aspects of algebra and logic \bookinfo Collected papers. Dedicated to Academician Sergei Ivanovich Adian on the occasion of his 80th birthday \serial Tr. Mat. Inst. Steklova \yr 2011 \vol 274 \pages 148--190 \publ MAIK Nauka/Interperiodica \publaddr Moscow \mathnet{http://mi.mathnet.ru/tm3318} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2962940} \transl \jour Proc. Steklov Inst. Math. \yr 2011 \vol 274 \pages 136--173 \crossref{https://doi.org/10.1134/S0081543811060101} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000295983200009} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84872941708} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Lysenok I., Ushakov A., “Spherical Quadratic Equations in Free Metabelian Groups”, Proc. Amer. Math. Soc., 144:4 (2016), 1383–1390
2. Lysenok I., Miasnikov A., Ushakov A., “Quadratic Equations in the Grigorchuk Group”, Group. Geom. Dyn., 10:1 (2016), 201–239
3. Kharlampovich O., Mohajeri A., Taam A., Vdovina A., “Quadratic Equations in Hyperbolic Groups Are Np-Complete”, Trans. Am. Math. Soc., 369:9 (2017), 6207–6238
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