English

MC-finiteness of restricted set partition functions

Combinatorics 2023-07-04 v4

Abstract

A sequence s(n)s(n) of integers is MC-finite if for every mN+m \in \mathbb{N}^+ the sequence sm(n)=s(n)modms^m(n) = s(n) \bmod{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.

Keywords

Cite

@article{arxiv.2302.08265,
  title  = {MC-finiteness of restricted set partition functions},
  author = {Yuval Filmus and Eldar Fischer and Johann A. Makowsky and Vsevolod Rakita},
  journal= {arXiv preprint arXiv:2302.08265},
  year   = {2023}
}

Comments

16 pages, 4 tables

R2 v1 2026-06-28T08:41:46.088Z