Deformation spaces of discrete groups and growth functions

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The head investigator Fujii obtained several results concerning pure Artin groups P of dihedral type. First, Fujii showed that the associated monoid is naturally embedded in P. Next, Fujii described a necessary and sufficient condition such that representatives of an element g of P are shotest among all representatives of g. Third, Fujii constructed a finite state automaton which accepts all the geodesic representatives of P, and obtained a rational function expression of the growth series for P. Moreover, Fujii showed that the growth rate of P is a Pisot number.