Linear recurrences indexed by $\mathbb{Z}$
Combinatorics
2021-10-12 v2 Rings and Algebras
Abstract
This note considers linear recurrences (also called linear difference equations) in unknowns indexed by the integers. We characterize a unique \emph{reduced} linear recurrence with the same solutions as a given linear recurrence, and construct a \emph{solution matrix} which parametrizes the space of solutions. Several properties of solution matrices are shown, including a combinatorial characterization of bases and dimension of the space of solutions.
Cite
@article{arxiv.1906.04311,
title = {Linear recurrences indexed by $\mathbb{Z}$},
author = {Greg Muller},
journal= {arXiv preprint arXiv:1906.04311},
year = {2021}
}
Comments
32 pages, best viewed in color v2) Added sections 9 and 10, containing several results related to twists of matrices