English

Recurrence Ranks and Moment Sequences

Combinatorics 2021-01-05 v1 Discrete Mathematics

Abstract

We introduce the "moment rank" and "unitary rank" of numerical sequences, close relatives of linear-recursive order. We show that both parameters can be characterized by a broad set of criteria involving moments of measures, types of recurrence relations, Hankel matrix factorizations, Waring rank, analytic properties of generating functions, and algebraic properties of polynomial ideals. In the process, we solve the "complex finite-atomic" and "integral finite-atomic" moment problems: which sequences arise as the moments of a finite-atomic complex-/integer-valued measures on C\mathbb{C}?

Keywords

Cite

@article{arxiv.2101.00302,
  title  = {Recurrence Ranks and Moment Sequences},
  author = {Joshua Cooper and Grant Fickes},
  journal= {arXiv preprint arXiv:2101.00302},
  year   = {2021}
}

Comments

21 pages, 0 figures

R2 v1 2026-06-23T21:41:32.566Z