Linear recurrences indexed by
arXiv:1906.04311
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.
32 pages, best viewed in color v2) Added sections 9 and 10, containing several results related to twists of matrices