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

In this paper we show the existence of families of triple or quadruple nested planar central configurations for the nn-body problem with n=6,8,9n=6,8,9. More precisely for n=6n=6 we nested three 2-collinear central configurations, for n=8n=8 we nested four 2-collinear central configurations and for n=9n=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.