On a family of Schreier graphs of intermediate growth associated with a self-similar group

详细信息    查看全文

• 作者：Ievgen Bondarenko^a ; ^{ibond.univ@gmail.com} ; Tullio Ceccherini-Silberstein^b ; ¹ ; ^{tceccher@mat.uniroma3.it} ; Alfredo Donno^c ; ^{alfredo.donno@sbai.uniroma1.it} ; Volodymyr Nekrashevych^d ; ^{nekrash@math.tamu.edu}
• 刊名：European Journal of Combinatorics
• 出版年：2012
• 出版时间：October, 2012
• 年：2012
• 卷：33
• 期：7
• 页码：1408-1421
• 全文大小：342 K

文摘

For every infinite sequence , with , we construct an infinite 4-regular graph . These graphs are precisely the Schreier graphs of the action of a certain self-similar group on the space . We solve the isomorphism and local isomorphism problems for these graphs, and determine their automorphism groups. Finally, we prove that all graphs have intermediate growth.