{"paper":{"title":"On minimal additive complements of integers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Csaba S\\'andor, Quan-Hui Yang, S\\'andor Z. Kiss","submitted_at":"2017-03-09T12:09:49Z","abstract_excerpt":"Let $C,W\\subseteq \\mathbb{Z}$. If $C+W=\\mathbb{Z}$, then the set $C$ is called an additive complement to $W$ in $\\mathbb{Z}$. If no proper subset of $C$ is an additive complement to $W$, then $C$ is called a minimal additive complement. Let $X\\subseteq \\mathbb{N}$. If there exists a positive integer $T$ such that $x+T\\in X$ for all sufficiently large integers $x\\in X$, then we call $X$ eventually periodic. In this paper, we study the existence of a minimal complement to $W$ when $W$ is eventually periodic or not. This partially answers a problem of Nathanson."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.03242","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}