Submission date: 5 August 2023

Abstract:

A sequence s(n) of integers is MC-finite if for every m ∈ N the sequence s^m (n) ≡ s(n) (mod m) is ultimately periodic. We discuss various ways of proving and disproving MC-finiteness. Our examples are mostly taken from set partition functions, but our methods can be applied to many more integer sequences.

Mathematics Subject Classification: Primary 05A99; Secondary 05A10, 05A18, 05A99, 03C13, 11Y55.

Keywords and phrases: Set Partition Function, C-Finiteness, MC,Fniteness, Supercon- gruence, Monadic Second Order Logic, Specker-Blatter Theorem.

Full text arXiv 2302.08265: pdf, ps.