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 ?
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