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Tr. Mat. Inst. Steklova, 2017, Volume 297, Pages 158–164 (Mi tm3840)  

This article is cited in 1 scientific paper (total in 1 paper)

Combinatorics of the subshift associated with Grigorchuk's group

Rostislav Grigorchukab, Daniel Lenzc, Tatiana Nagnibedad

a Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA
b Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
c Institut für Mathematik, Friedrich-Schiller-Universität Jena, 07743 Jena, Germany
d Section de Mathématiques, Université de Genève, 2-4 rue du Lièvre, Case postale 64, 1211 Geneva 4, Switzerland

Abstract: 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.

Funding Agency Grant Number
Swiss National Science Foundation
National Science Foundation DMS-1207669
European Research Council AG COMPASP
The authors acknowledge support of the Swiss National Science Foundation. The first author was also supported in part by the NSF grant DMS-1207669 and by ERC AG COMPASP.


DOI: https://doi.org/10.1134/S037196851702008X

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English version:
Proceedings of the Steklov Institute of Mathematics, 2017, 297, 138–144

Bibliographic databases:

UDC: 517.938+512.54
Received: February 19, 2017

Citation: Rostislav Grigorchuk, Daniel Lenz, Tatiana Nagnibeda, “Combinatorics of the subshift associated with Grigorchuk's group”, Order and chaos in dynamical systems, Collected papers. On the occasion of the 125th anniversary of the birth of Academician Dmitry Victorovich Anosov, Tr. Mat. Inst. Steklova, 297, MAIK Nauka/Interperiodica, Moscow, 2017, 158–164; Proc. Steklov Inst. Math., 297 (2017), 138–144

Citation in format AMSBIB
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\paper Combinatorics of the subshift associated with Grigorchuk's group
\inbook Order and chaos in dynamical systems
\bookinfo Collected papers. On the occasion of the 125th anniversary of the birth of Academician Dmitry Victorovich Anosov
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\vol 297
\pages 158--164
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Grigorchuk R., Lenz D., Nagnibeda T., “Schreier Graphs of Grigorchuk'S Group and a Subshift Associated to a Nonprimitive Substitution”, Groups, Graphs and Random Walks, London Mathematical Society Lecture Note Series, 436, eds. CeccheriniSilberstein T., Salvatori M., SavaHuss E., Cambridge Univ Press, 2017, 250–299  mathscinet  zmath  isi
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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