On Positivity and Minimality for Second-Order Holonomic Sequences
George Kenison, Oleksiy Klurman, Engel Lefaucheux, Florian Luca, Pieter Moree, Joël Ouaknine, Markus Whiteland and James Worrell
An infinite sequence
In this paper we give a Turing reduction of the problem of deciding positivity of second-order holonomic sequences to that of deciding minimality of such sequences. More specifically, we give a procedure for determining positivity of second-order holonomic sequences that terminates in all but an exceptional number of cases, and we show that in these exceptional cases positivity can be determined using an oracle for deciding minimality.