PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

Partitions of natural numbers with the same weighted representation functions

Volume 159 / 2020

Ya-Li Li, Wu-Xia Ma Colloquium Mathematicum 159 (2020), 1-5 MSC: Primary 11B34; Secondary 05A17. DOI: 10.4064/cm7605-11-2018 Published online: 6 September 2019


For a set $A$ of nonnegative integers and two positive integers $k_1, k_2$, let $r_{k_1,k_2}(A,n)$ be the number of solutions of $n=k_1a_1+k_2a_2$, where $a_1, a_2\in A$. In 2012, Yang and Chen determined all pairs $k_1$ and $k_2$ for which there exists a set $A$ of nonnegative integers such that $r_{k_1,k_2}(A, n)=r_{k_1,k_2}(\mathbb {N}\setminus A,n)$ for all sufficiently large integers $n$. We use generating functions to give new proofs of the results by Yang and Chen.


  • Ya-Li LiSchool of Mathematics and Statistics
    Henan University
    Kaifeng 475001, P.R. China
  • Wu-Xia MaSchool of Mathematical Sciences
    and Institute of Mathematics
    Nanjing Normal University
    Nanjing 210023, P.R. China

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image