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5
questions
4
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233
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How to find generators of translation subgroup of an abstract reflection (coxeter) group
I have an infinite reflection group https://en.wikipedia.org/wiki/Coxeter_group
Take for example the affine groups $[4,4],[4,3,4],[4,3,3,4]$...
I'd like to get an explicit expression for generators ...
- 1,010
7
votes
1
answer
399
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On groups with presentations $ \langle a,b,c\mid a^2=b^2=c^2=(ab)^p=(bc)^q=(ca)^r=(abc)^s=1\rangle $...
$$
\langle a,b,c\mid a^2=b^2=c^2=(ab)^p=(bc)^q=(ca)^r=1\rangle =\Delta(p,q,r)
$$
This is a presentation of a triangle group $\Delta(p,q,r)$, a special kind of Coxeter group.
EDIT In fact, these are ...
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5
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0
answers
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Mapping $\Delta(2,2,2)\mapsto \Delta(4,4,2)$... [closed]
Looking at the images below, you recognize that the adajency matrix of the graph $A_G$ splits up into three different color submatrices, with $A_G=A_r+A_b+A_d$ (where $d$ is dark, damn...).
It's ...
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4
votes
1
answer
499
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Coxeter presentation of Hyperoctahedral group $(\mathbb{Z}/2\mathbb{Z})^n \rtimes S_n$.
I know that the hyperoctahedral group $(\mathbb{Z}/2\mathbb{Z})^n \rtimes S_n$ has the presentation
$$\langle s_{\text{1}},\ldots,s_n\mid s_{\text{1}}^{\text{2}}=s_i^2=1, (s_1s_2)^4=(s_is_{i+1})^3=(...
- 1,810
3
votes
0
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About the order of Coxeter groups
I have a question about Coxeter groups with $3$ generators:
Suppose, as a group, $G$ is generated by $a,b$ and $c$, with the relations $a^2 =b^2 =c^2 =1$, $(ab)^m = (bc)^n = (ca)^p =1$ where $2 \...
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