Triple and quadruple nested central configurations for the planar -body problem

In this paper we show the existence of families of triple or quadruple nested planar central configurations for the n -body problem with n = 6 , 8 , 9 . More precisely for n = 6 we nested three 2-collinear central configurations, for n = 8 we nested four 2-collinear central configurations and for n = 9 we nested three equilateral triangular central configurations. As far as we know these are the first examples of planar triple and quadruple nested central configurations.