Výsledky vyhledávání - "Alexey Talambutsa"

On Subquadratic Derivational Complexity of Semi-Thue Systems

Autor: Alexey Talambutsa

Publikováno v: Computer Science – Theory and Applications ISBN: 9783030500252
CSR

We prove that for any rational number $\alpha >1$ there exists a semi-Thue system with derivational complexity function belonging to the asymptotic class $\varTheta (n^{\alpha })$. In particular, we answer a question of Y. Kobayashi, whether ther

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::35473f9a09d34f7a70b1c4efe453d431
https://doi.org/10.1007/978-3-030-50026-9_28

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Growth rates of Coxeter groups and Perron numbers

Autor: Alexey Talambutsa, Alexander Kolpakov

We define a large class of abstract Coxeter groups, that we call $\infty$--spanned, and for which the word growth rate and the geodesic growth rate appear to be Perron numbers. This class contains a fair amount of Coxeter groups acting on hyperbolic

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5aba5c0b421450e2e85968821b06b02c
http://arxiv.org/abs/1912.05608

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Minimal exponential growth rates of metabelian Baumslag–Solitar groups and lamplighter groups

Autor: Alexey Talambutsa, Michelle Bucher

Publikováno v: Groups, Geometry, and Dynamics. 11:189-209

We prove that for any prime $p\geq 3$ the minimal exponential growth rate of the Baumslag-Solitar group $BS(1,p)$ and the lamplighter group $\mathcal{L}_p=(\mathbb{Z}/p\mathbb{Z})\wr \mathbb{Z}$ are equal. We also show that for $p=2$ this claim is no

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::b7ff757244d6db89782cc964a6e28491
https://doi.org/10.4171/ggd/394

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Exponential growth rates of free and amalgamated products

Autor: Michelle Bucher, Alexey Talambutsa

Publikováno v: Israel Journal of Mathematics. 212:521-546

We prove that there is a gap between $\sqrt{2}$ and $(1+\sqrt{5})/2$ for the exponential growth rate of free products $G=A*B$ not isomorphic to the infinite dihedral group. For amalgamated products $G=A*_C B$ with $([A:C]-1)([B:C]-1)\geq2$, we show t

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::64c5bd5316c103b4bd3b99cacddfa81f
https://doi.org/10.1007/s11856-016-1299-4

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Spherical and geodesic growth rates of right-angled Coxeter and Artin groups are Perron numbers

Autor: Alexey Talambutsa, Alexander Kolpakov

Publikováno v: Discrete Mathematics. 343:111763

We prove that for any infinite right-angled Coxeter or Artin group, its spherical and geodesic growth rates (with respect to the standard generating set) either take values in the set of Perron numbers, or equal 1. Also, we compute the average number

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::c17430a7b887a572d0054ec42903353f
https://doi.org/10.1016/j.disc.2019.111763

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Attainability of the minimal exponential growth rate for free products of finite cyclic groups

Autor: Alexey Talambutsa

Publikováno v: Proceedings of the Steklov Institute of Mathematics. 274:289-302

We consider free products of two finite cyclic groups of orders 2 and n, where n is a prime power. For any such group ℤ2 * ℤn = 〈a, b | a2 = bn = 1〉, we prove that the minimal growth rate αn is attained on the set of generators {a, b} and ex

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::6ab8d0cebd4696ddcd3bf6fd0a6dee2a
https://doi.org/10.1134/s0081543811060186

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