On a problem of minimal additive complements for not eventually periodic $S$-difference sets

Min Tang; Wenjing He

number theory

On a problem of minimal additive complements for not eventually periodic $S$ -difference sets

arXiv:2607.27059

summary

The paper proves a conjecture of Ma and Chen by showing that for certain integer sets whose S‑difference sets are not eventually periodic, minimal additive complements exist.

Abstract

Let $C$ and $W$ be two integer sets. If $C + W = Z$ , then we say that $C$ is an additive complement to $W$ . If no proper subset of $C$ is an additive complement to $W$ , then we say that $C$ is a minimal additive complement to $W$ . In this paper, we give an affirmative answer to one problem of Ma and Chen [On a problem of minimal additive complements of integers, J. Number Theory 284(2026), 178-187.]

Topics & keywords

#additive number theory #minimal additive complements #integer sets #periodicity #combinatorial number theoryadditive complementminimal additive complementS-difference seteventually periodicinteger sets

On a problem of minimal additive complements for not eventually periodic S-difference sets

Abstract

Topics & keywords

On a problem of minimal additive complements for not eventually periodic $S$ -difference sets