BUSEMANN POINTS OF ARTIN GROUPS OF DIHEDRAL TYPE
نویسندگان
چکیده
منابع مشابه
Busemann Points of Artin Groups of dihedral Type
We study the horofunction boundary of an Artin group of dihedral type with its word metric coming from either the usual Artin generators or the dual generators. In both cases, we determine the horoboundary and say which points are Busemann points, that is the limits of geodesic rays. In the case of the dual generators, it turns out that all boundary points are Busemann points, but this is not t...
متن کاملThe growth rates for pure Artin groups of dihedral type
We consider the kernel of the natural projection from the Artin group of dihedral type I2(k) to the associated Coxeter group, which we call a pure Artin group of dihedral type and write PI2(k). We show that the growth rates for both the spherical growth series and geodesic growth series of PI2(k) with respect to a natural generating set are Pisot numbers. 2010 Mathematics Subject Classification...
متن کاملGrowth Series for Artin Groups of Dihedral Type
We consider the Artin groups of dihedral type I2(k) defined by the presentation Ak = 〈a, b | prod(a, b; k) = prod(b, a; k)〉 where prod(s, t; k) = ststs..., with k terms in the product on the right-hand side. We prove that the spherical growth series and the geodesic growth series of Ak with respect to the Artin generators {a, b, a, b−1} are rational. We provide explicit formulas for the series.
متن کاملArtin groups of euclidean type
Coxeter groups were introduced by Jacques Tits in the 1960s as a natural generalization of the groups generated by reflections which act geometrically (which means properly discontinuously cocompactly by isometries) on spheres and euclidean spaces. And ever since their introduction their basic structure has been reasonably well understood [BB05, Bou02, Dav08]. More precisely, every Coxeter grou...
متن کاملCalculations of Dihedral Groups Using Circular Indexation
In this work, a regular polygon with $n$ sides is described by a periodic (circular) sequence with period $n$. Each element of the sequence represents a vertex of the polygon. Each symmetry of the polygon is the rotation of the polygon around the center-point and/or flipping around a symmetry axis. Here each symmetry is considered as a system that takes an input circular sequence and g...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Journal of Algebra and Computation
سال: 2009
ISSN: 0218-1967,1793-6500
DOI: 10.1142/s0218196709005391