Orbit-blocking words in free groups

References

[1] D. Ascari, A fine property of Whitehead’s algorithm, Groups Geom. Dyn. 18 (2024), no. 1, 235–264. 10.4171/ggd/746Search in Google Scholar

[2] V. Bardakov, V. Shpilrain and V. Tolstykh, On the palindromic and primitive widths of a free group, J. Algebra 285 (2005), no. 2, 574–585. 10.1016/j.jalgebra.2004.11.003Search in Google Scholar

[3] G. Baumslag, A. G. Myasnikov and V. Shpilrain, Open problems in combinatorial group theory, http://shpilrain.ccny.cuny.edu/gworld/problems/oproblems.html. Search in Google Scholar

[4] T. Ceccherini-Silberstein and W. Woess, Growth and ergodicity of context-free languages, Trans. Amer. Math. Soc. 354 (2002), no. 11, 4597–4625. 10.1090/S0002-9947-02-03048-9Search in Google Scholar

[5] M. Cohen, W. Metzler and A. Zimmermann, What does a basis of F ⁢ ( a , b ) look like?, Math. Ann. 257 (1981), no. 4, 435–445. 10.1007/BF01465865Search in Google Scholar

[6] M. Heusener and R. Weidmann, A remark on Whitehead’s cut-vertex lemma, J. Group Theory 22 (2019), no. 1, 15–21. 10.1515/jgth-2018-0118Search in Google Scholar

[7] L. Hyde, S. O’Connor and V. Shpilrain, Orbit-blocking words and the average-case complexity of Whitehead’s problem in the free group of rank 2, J. Group Theory 28 (2025), no. 2, 423–430. 10.1515/jgth-2024-0140Search in Google Scholar

[8] I. Kapovich, A. Miasnikov, P. Schupp and V. Shpilrain, Average-case complexity and decision problems in group theory, Adv. Math. 190 (2005), no. 2, 343–359. 10.1016/j.aim.2003.02.001Search in Google Scholar

[9] 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 (2006), no. 1, 113–140. 10.2140/pjm.2006.223.113Search in Google Scholar

[10] B. Khan, The structure of automorphic conjugacy in the free group of rank two, Computational and Experimental Group Theory, Contemp. Math. 349, American Mathematical Society, Providence (2004), 115–196. 10.1090/conm/349/06360Search in Google Scholar

[11] D. E. Knuth, J. H. Morris, Jr. and V. R. Pratt, Fast pattern matching in strings, SIAM J. Comput. 6 (1977), no. 2, 323–350. 10.1137/0206024Search in Google Scholar

[12] A. G. Myasnikov and V. Shpilrain, Automorphic orbits in free groups, J. Algebra 269 (2003), no. 1, 18–27. 10.1016/S0021-8693(03)00339-9Search in Google Scholar

[13] V. Shpilrain, Average-case complexity of the Whitehead problem for free groups, Comm. Algebra 51 (2023), no. 2, 799–806. 10.1080/00927872.2022.2113791Search in Google Scholar

[14] J. H. C. Whitehead, On certain sets of elements in a free group, Proc. Lond. Math. Soc. (2) 41 (1936), no. 1, 48–56. 10.1112/plms/s2-41.1.48Search in Google Scholar

[15] J. H. C. Whitehead, On equivalent sets of elements in a free group, Ann. of Math. (2) 37 (1936), no. 4, 782–800. 10.2307/1968618Search in Google Scholar

[16] Wikipedia Contributors, Double-ended queue, Wikipedia (2024), https://en.wikipedia.org/w/index.php?title=Double-ended_queue&oldid=1225841227. Search in Google Scholar