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

TL;DR

This paper introduces a new concept of polynomial generations where each subsequent polynomial's coefficients are the zeros of the previous, leading to the discovery of new solvable many-body problems of 'goldfish type'.

Contribution

It presents a novel framework linking polynomial generations to the construction of new exactly solvable many-body systems.

Findings

Defined generations of monic polynomials with recursive zero-coefficient relations

Established connection to solvable many-body problems of 'goldfish type'

Demonstrated relevance to integrable systems theory

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.