Geodesic
Combinatorics of the subshift associated with Grigorchuk's group
Informatics and Automation, Order and chaos in dynamical systems, Tome 297 (2017), pp. 158-164.

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We study combinatorial properties of the subshift induced by the substitution that describes Lysenok's presentation of Grigorchuk's group of intermediate growth by generators and relators. This subshift has recently appeared in two different contexts: on the one hand, it allowed embedding Grigorchuk's group in a topological full group, and on the other hand, it was useful in the spectral theory of Laplacians on the associated Schreier graphs. 
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Rostislav Grigorchuk; Daniel Lenz; Tatiana Nagnibeda. Combinatorics of the subshift associated with Grigorchuk's group. Informatics and Automation, Order and chaos in dynamical systems, Tome 297 (2017), pp. 158-164. http://geodesic.mathdoc.fr/item/TRSPY_2017_297_a7/

[1] Baake M., Grimm U., Aperiodic order, v. 1, Encycl. Math. Appl., 149, A mathematical invitation, Cambridge Univ. Press, Cambridge, 2014 | MR

[2] Grigorchuk R. I., “K probleme Bernsaida o periodicheskikh gruppakh”, Funkts. analiz i ego pril., 14:1 (1980), 53–54 | MR | Zbl

[3] Grigorchuk R. I., “Stepeni rosta konechno-porozhdennykh grupp i teoriya invariantnykh srednikh”, Izv. AN SSSR. Ser. mat., 48:5 (1984), 939–985 | MR | Zbl

[4] Grigorchuk R., Lenz D., Nagnibeda T., Spectra of Schreier graphs of Grigorchuk's group and Schroedinger operators with aperiodic order, E-print, 2014, arXiv: 1412.6822[math.GR]

[5] Grigorchuk R., Lenz D., Nagnibeda T., “Schreier graphs of Grigorchuk's group and a subshift associated to a non-primitive substitution”, Groups, graphs and random walks, LMS Lect. Note Ser., 436, eds. T. Ceccherini-Silberstein, M. Salvatori, E. Sava-Huss, Cambridge Univ. Press, Cambridge, 2017 | MR

[6] Lysënok I. G., “Sistema opredelyayuschikh sootnoshenii dlya gruppy Grigorchuka”, Mat. zametki, 38:4 (1985), 503–516 | MR | Zbl

[7] J. Kellendonk, D. Lenz, J. Savinien (eds.), Mathematics of aperiodic order, Prog. Math., 309, Birkhäuser, Basel, 2015 | DOI | MR | Zbl

[8] Matte Bon N., “Topological full groups of minimal subshifts with subgroups of intermediate growth”, J. Mod. Dyn., 9 (2015), 67–80 | DOI | MR | Zbl

[9] Nekrashevych V., Palindromic subshifts and simple periodic groups of intermediate growth, E-print, 2016, arXiv: 1601.01033[math.GR]

[10] Walters P., An introduction to ergodic theory, Grad. Texts Math., 79, Springer, New York, 1982 | DOI | MR | Zbl