arXiv math/05045662005-04-28math.GRmath.MG

Embedding of hyperbolic Coxeter groups into products of binary trees and aperiodic tilings

Alexander Dranishnikov, Viktor Schroeder

英文摘要：

We prove that a finitely generated, right-angled, hyperbolic Coxeter group can be quasiisometrically embedded into the product of n binary trees, where n is the chromatic number of the group. As application we obtain certain strongly aperiodic tilings of the Davis complex of these groups.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Aperiodic colorings and tilings of Coxeter groups

We construct a limit aperiodic coloring of hyperbolic groups. Also we construct limit strongly aperiodic strictly balanced tilings of the Davis complex for all Coxeter groups.

2007-03-30math.GRmath.MG

Aperiodic tilings of manifolds of intermediate growth

We give a homological construction of aperiodic tiles for certain open Riemannian surfaces admitting actions of Grigorchuk groups of intermediate growth.

2013-02-18math.DSmath.GRmath.GT

Homological aperiodic tilings of 3-dimensional geometries

We construct the first aperiodic tiles for two amenable 3-dimensional Lie groups: Sol and the Heisenberg group. Our construction relies on the use of higher-dimensional uniformly finite homology. In particular, we settle completely the existence of aperiodic tiles for all of the non-compact geometries of 3-manifolds appearing in the geometrization conjecture.

2012-05-16math.DSmath.GRmath.GT

Subtilings of Elnitsky Tilings for Finite Irreducible Coxeter Groups

Two new Elnitsky tilings for Coxeter groups of type $\mathrm{B}$ are displayed as certain subtilings. Additionally, a new tiling for the non-crystallographic Coxeter group of type $\mathrm{H}_3$ is obtained, described as a $\mathrm{D}_6$-subtiling.

2021-06-06math.COmath.GR

有限Coxeter群与广义Elnitsky铺砌

Finite Coxeter Groups and Generalized Elnitsky Tilings

本文基于Elnitsky对A、B、D型Coxeter群约化词与多边形铺砌的双射，通过嵌入对称群的方法，将其推广至所有有限Coxeter群。

2024-07-20math.COmath.GR

有限Coxeter群的Bruhat序与Elnitsky铺砌

The Bruhat Order of a Finite Coxeter Group and Elnitsky Tilings

本文证明有限Coxeter群中任意元素及其约化表达式对应一个2m-多边形的Elnitsky铺砌，其中m为子群指数，构造性证明结合E-嵌入与删除序，并给出E8等示例。

2024-07-20math.GR

更多相关论文收起更多论文

Tilings of the hyperbolic plane of substitutive origin as subshifts of finite type on Baumslag-Solitar groups $BS(1,n)$

We present a technique to lift some tilings of the discrete hyperbolic plane -- tilings defined by a 1D substitution -- into a zero entropy subshift of finite type (SFT) on non-abelian amenable Baumslag-Solitar groups $BS(1,n)$ for $n\geq2$. For well chosen hyperbolic tilings, this SFT is also aperiodic and minimal. As an application we construct a strongly aperiodic SFT on $BS(1,n)$ with a hierarchical structure, which is an analogue of Robinson's construction on $\mathbb{Z}^2$ or Goodman-Strauss's on $\mathbb{H}_2$.

2020-12-20cs.DMmath.DSmath.GR

Addendum to "Tilings problems on Baumslag-Solitar groups"

In our article in MCU'2013 we state the the Domino problem is undecidable for all Baumslag-Solitar groups $BS(m,n)$, and claim that the proof is a direct adaptation of the construction of a weakly aperiodic subshift of finite type for $BS(m,n)$ given in the paper. In this addendum, we clarify this point and give a detailed proof of the undecidability result. We assume the reader is already familiar with the article in MCU'2013.

2021-01-29cs.DMmath.DSmath.GR

删除序与Coxeter群

The Deletion Order and Coxeter Groups

本文研究有限生成Coxeter群的删除序，证明其为Bruhat序的加细，定义了对应范式并证明与从右到左字典序范式一致，还得到了其Artin性质及与有限Coxeter群最长元素的相互作用等结果。

2025-02-22math.COmath.GR