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. 
@article{TRSPY_2017_297_a7,
     author = {Rostislav Grigorchuk and Daniel Lenz and Tatiana Nagnibeda},
     title = {Combinatorics of the subshift associated with {Grigorchuk's} group},
     journal = {Informatics and Automation},
     pages = {158--164},
     publisher = {mathdoc},
     volume = {297},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2017_297_a7/}
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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/