Universality of representing power-sum sequences as supersymmetric Newton sums

Determine whether every sequence of power-sum variables p = (p1, p2, p3, …) can be represented in the form p_n = ∑_{i=1}^N (a_i^n − (−b_i)^n) for all n ≥ 1, for some integer N (possibly infinite) and complex sequences a = (a_1, …, a_N) and b = (b_1, …, b_N). Equivalently, ascertain whether any choice of power-sum data admits a realization as the supersymmetric Newton sums p(a/−b).

Background

The paper introduces the supersymmetric Newton sums parameterization p(a/−b), defined by p_n(a/−b) = ∑_{i=1}^N (a_i^n − (−b_i)^n), and uses it systematically to relate KP tau functions and correlators to BKP tau functions and correlators.

The author explicitly notes a conjectural universality: that any sequence of power-sum variables p might be realized as p(a/−b) for some N and coordinate sets a and b. Establishing this would justify the generality of the chosen parameterization and underpin the broad applicability of the bilinear KP–BKP relations developed in the paper.