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 
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/
@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},
     year = {2017},
     volume = {297},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2017_297_a7/}
}
TY  - JOUR
AU  - Rostislav Grigorchuk
AU  - Daniel Lenz
AU  - Tatiana Nagnibeda
TI  - Combinatorics of the subshift associated with Grigorchuk's group
JO  - Informatics and Automation
PY  - 2017
SP  - 158
EP  - 164
VL  - 297
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2017_297_a7/
LA  - ru
ID  - TRSPY_2017_297_a7
ER  - 
%0 Journal Article
%A Rostislav Grigorchuk
%A Daniel Lenz
%A Tatiana Nagnibeda
%T Combinatorics of the subshift associated with Grigorchuk's group
%J Informatics and Automation
%D 2017
%P 158-164
%V 297
%U http://geodesic.mathdoc.fr/item/TRSPY_2017_297_a7/
%G ru
%F TRSPY_2017_297_a7

Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[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