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A good reference is Brown's article Finiteness properties of groups (1987). Section 4 of the paper defines and describes carefully the groups $G_{n,r}$, now referred to as Higman-Thompson groups. Actually, the section provides a good general introduction to Thompson groups. This also the first place where the groups $F_{n,r}$ and $T_{n,r}$ appear. On pages 54-55, there are some interesting historical remarks.