Work

Extending Arithmetic Properties for Compositions Wherein Parts That Are Non-Multiples of k Can Be of t Kinds

Year: 2026

Type: article

Abstract: In two papers published in Quaestiones Mathematicae , Munagi and Sellers considered the family of functions $$D_{k,t}(n)$$ D k , t ( n ) that count the number of integer compositions of weight n in which parts not divisible by k can be of t kinds (subscripted $$0, 1, \dots ,t-1$$ 0 , 1 , ⋯ , t - 1 ). These are also closely related to “inplace” integer compositions of weight n . In their second paper, Munagi and Sellers proved a few divisibility properties satisfied by $$D_{k,t}(n)$$ D k , t ( n ) for specific values of k , t , and n . In this work, we significantly extend these arithmetic properties, providing infinitely families of congruences. Our proof techniques are quite elementary, relying on the structure of the generating functions in question.

Source: Periodica Mathematica Hungarica

DOI: 10.1007/s10998-026-00714-z

Authors: László Németh, James A. Sellers, László Szalay

Institutions: University of Sopron, University of Minnesota, Duluth, J. Selye University

Language: English

Topic: Advanced Mathematical Identities

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funder: Soproni Egyetem