On Rational Recursion for Holonomic Sequences
arxiv(2024)
摘要
It was recently conjectured that every component of a discrete rational
dynamical system is a solution to an algebraic difference equation that is
linear in its highest-shift term (a quasi-linear equation). Holonomic sequences
are trivially seen as solutions to such dynamical systems. We prove that the
conjecture holds for holonomic sequences and propose two algorithms for
converting holonomic recurrence equations into such quasi-linear equations. The
two algorithms differ in their efficiency and the minimality of orders in their
outputs.
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