{"paper":{"title":"Finite Representability of Integers as $2$-Sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Anant Godbole, Zach Higgins, Zoe Koch","submitted_at":"2017-05-15T12:53:01Z","abstract_excerpt":"A set $\\mathcal{A}$ is said to be an additive $h$-basis if each element in $\\{0,1,\\ldots,hn\\}$ can be written as an $h$-sum of elements of $\\mathcal{A}$ in {\\it at least} one way. We seek multiple representations as $h$-sums, and, in this paper we make a start by restricting ourselves to $h=2$. We say that $\\mathcal{A}$ is said to be a truncated $(\\alpha,2,g)$ additive basis if each $j\\in[\\alpha n, (2-\\alpha)n]$ can be represented as a $2$-sum of elements of $\\mathcal{A}$ in at least $g$ ways. In this paper, we provide sharp asymptotics for the event that a randomly selected set is a truncated"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.05198","kind":"arxiv","version":1},"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"}