Rewriting Systems and the Complete Growth Series for Triangular Coxeter Groups
Matematičeskie zametki, Tome 71 (2002) no. 3, pp. 431-439

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In this paper, a complete finite rewriting system is constructed for Coxeter groups of the form $$ W=\langle a,b,c\mid a^2=b^2=c^2=(ab)^p=(bc)^q=(ca)^r=1\rangle $$ with respect to the system of generators $S=\{a,b,c\}$, where $p,q,r\in \mathbb Z$, $p,q,r\ge 2$ and $1/p+1/q+1/r1$. Rewriting systems of this kind can be used to evaluate the complete growth series of a group.
@article{MZM_2002_71_3_a8,
     author = {M. D. Mamaghani},
     title = {Rewriting {Systems} and the {Complete} {Growth} {Series} for {Triangular} {Coxeter} {Groups}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {431--439},
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     volume = {71},
     number = {3},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2002_71_3_a8/}
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M. D. Mamaghani. Rewriting Systems and the Complete Growth Series for Triangular Coxeter Groups. Matematičeskie zametki, Tome 71 (2002) no. 3, pp. 431-439. http://geodesic.mathdoc.fr/item/MZM_2002_71_3_a8/