Journal of Integer Sequences, Vol. 26 (2023), Article 23.7.4

MC-Finiteness of Restricted Set Partition Functions


Yuval Filmus, Eldar Fischer, and Johann A. Makowsky
Faculty of Computer Science
Israel Institute of Technology
3200003 Haifa
Israel

Vsevolod Rakita
Faculty of Mathematics
Israel Institute of Technology
3200003 Haifa
Israel

Abstract:

A sequence s(n) of integers is MC-finite if for every m ∈ N the sequence 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.

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(Concerned with sequences A000108 A000110 A000453 A000587 A000670 A000798 A001035 A001286 A001861 A005493 A005494 A006789 A006905 A086714 A110040 A143494 A143495 A143496 A143497 A232472 A295193.)

Received February 19 2023; revised versions received February 20 2023; June 10 2023; June 11 2023; July 3 2023; July 16 2023; August 2 2023; August 3 2023. Published in Journal of Integer Sequences, August 4 2023.

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