Linear recurrences indexed by ℤ

2019/06/10 by Muller, Greg
#15A06 #15A15 #Combinatorics (math.CO) #FOS: Mathematics #Primary 39A Secondary 11B37 #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1906.04311

Abstract

This note considers linear recurrences (also called linear difference equations) in unknowns indexed by the integers. We characterize a unique reduced linear recurrence with the same solutions as a given linear recurrence, and construct a 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.

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