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Experimental Mathematics Volume 16, 2007 - Issue 1
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Original Article

Clusters, Currents, and Whitehead's Algorithm

Ilya Kapovich Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, IL 61801
Pages 67-76 | Published online: 30 Jan 2011

  • S. Francaviglia. "Geodesic Currents and Length Compactness for Automorphisms of Free Groups." arXiv:math.GR/0602555, 2006.
  • R. Haralick, A. D. Miasnikov, and A. G. Myasnikov. "Pattern Recognition Approaches to Solving Combinatorial Problems in Free groups." In Computational and Experimental Group Theory, pp. 197–213, Contemp. Math. 349. Providence: Amer. Math. Soc., 2004.
  • R. Haralick, A. D. Miasnikov, and A. G. Myasnikov. "Pattern Recognition and Minimal Words in Free Groups of Rank 2." J. Group Theory 8:4 (2005), 523–538.
  • R. Haralick, A. D. Miasnikov, and A. G. Myasnikov. "Heuristics for the Whitehead Minimization Problem." Experiment. Math. 14:1 (2005), 7–14.
  • V. Kaimanovich, I. Kapovich, and P. Schupp. "The Subadditive Ergodic Theorem and Generic Stretching Factors for Free Group Automorphisms." To appear in Israel J. Math., arXiv:math.GR/0504105, 2005.
  • I. Kapovich, "The Frequency Space of a Free Group." Internat. J. Alg. Comput. (special Gaeta Grigorchuk 50th birthday issue) 15:5–6 (2005), 939–969.
  • I. Kapovich, "Currents on Free Groups." In Topological and Asymptotic Aspects of Group Theory, edited by R. Grigorchuk, M. Mihalik, M. Sapir, and Z. Sunik, pp. 149–176, AMS Contemporary Mathematics Series 394. Providence: Amer. Math. Soc., 2006.
  • I. Kapovich, A. Myasnikov, P. Schupp, and V. Shpilrain. "Generic-Case Complexity, Decision Problems in Group Theory and Random Walks." J. Algebra 264:2 (2003), 665–694.
  • I. Kapovich, P. Schupp, and V. Shpilrain. "Generic Properties of Whitehead's Algorithm and Isomorphism Rigidity of Random One-Relator Groups." Pacific J. Math. 223:1 (2006), 113–140.
  • B. Khan. "The Structure of Automorphic Conjugacy in the Free Group of Rank Two." In Computational and Experimental Group Theory, pp. 115–196, Contemp. Math. 349. Providence: Amer. Math. Soc., 2004.
  • D. Lee. "Counting Words of Minimum Length in an Automorphic Orbit." J. Algebra 301:1 (2006), 35–38.
  • R. Lyndon and P. Schupp. Combinatorial Group Theory. New York: Springer-Verlag, 1977.
  • R. Martin. "Non-Uniquely Ergodic Foliations of Thin Type, Measured Currents and Automorphisms of Free Groups." PhD diss., UCLA, 1995.
  • A. G. Myasnikov and V. Shpilrain. "Automorphic Orbits in Free Groups." J. Algebra 269:1 (2003), 18–27.
  • J. H. C. Whitehead. "On Equivalent Sets of Elements in Free Groups." Annals of Mathematics 37 (1936), 782–800.

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