MC-Finiteness of Restricted Set Partition Functions

Yuval Filmus; Eldar Fischer; Johann A. Makowsky; Vsevolod Rakita

MC-Finiteness of Restricted Set Partition Functions

Yuval Filmus, Eldar Fischer, Johann A. Makowsky, Vsevolod Rakita

Computer Science

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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 MCfiniteness. Our examples are mostly taken from set partition functions, but our methods can be applied to many more integer sequences.

Original language	English
Article number	23.7.4
Journal	Journal of Integer Sequences
Volume	26
Issue number	7
State	Published - 2023

Keywords

C-Finiteness
MC
Specker-Blatter theorem
finiteness
monadic second-order logic
set partition function
supercongruence

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

Cite this

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title = "MC-Finiteness of Restricted Set Partition Functions",

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 MCfiniteness. Our examples are mostly taken from set partition functions, but our methods can be applied to many more integer sequences.",

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AU - Fischer, Eldar

AU - Makowsky, Johann A.

AU - Rakita, Vsevolod

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Y1 - 2023

N2 - 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 MCfiniteness. Our examples are mostly taken from set partition functions, but our methods can be applied to many more integer sequences.

AB - 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 MCfiniteness. Our examples are mostly taken from set partition functions, but our methods can be applied to many more integer sequences.

KW - C-Finiteness

KW - MC

KW - Specker-Blatter theorem

KW - finiteness

KW - monadic second-order logic

KW - set partition function

KW - supercongruence

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MC-Finiteness of Restricted Set Partition Functions

Abstract

Keywords

ASJC Scopus subject areas

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