Generations of monic polynomials such that the coefficients of the polynomials of the next generation coincide with the zeros of the polynomials of the current generation, and new solvable many-body problems

Abstract: The notion of generations of monic polynomials such that the coefficients of the polynomials of the next generation coincide with the zeros of the polynomials of the current generation is introduced, and its relevance to the identification of endless sequences of new solvable many-body problems of "goldfish type" is demonstrated.