Details

Autor(en) / Beteiligte

• YAN, XIAO-HUI

Titel

ON PARTITIONS OF NONNEGATIVE INTEGERS AND REPRESENTATION FUNCTIONS

Ist Teil von

• Bulletin of the Australian Mathematical Society, 2019-06, Vol.99 (3), p.385-387

Ort / Verlag

Cambridge, UK: Cambridge University Press

Erscheinungsjahr

2019

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• Let $\mathbb{N}$ be the set of all nonnegative integers. For any set $A\subset \mathbb{N}$ , let $R(A,n)$ denote the number of representations of $n$ as $n=a+a^{\prime }$ with $a,a^{\prime }\in A$ . There is no partition $\mathbb{N}=A\cup B$ such that $R(A,n)=R(B,n)$ for all sufficiently large integers  $n$ . We prove that a partition $\mathbb{N}=A\cup B$ satisfies $|R(A,n)-R(B,n)|\leq 1$ for all nonnegative integers $n$ if and only if, for each nonnegative integer  $m$ , exactly one of $2m+1$ and $2m$ is in  $A$ .