{"paper":{"title":"Logarithmic Representability of Integers as k-Sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anant P. Godbole, Samuel Gutekunst, Vince Lyzinski, Yan Zhuang","submitted_at":"2013-02-07T17:33:30Z","abstract_excerpt":"A set A=A_{k,n} in [n]\\cup{0} is said to be an additive k-basis if each element in {0,1,...,kn} can be written as a k-sum of elements of A in at least one way. Seeking multiple representations as k-sums, and given any function phi(n), with lim(phi(n))=infinity, we say that A is a truncated phi(n)-representative k-basis for [n] if for each j in [alpha n, (k-alpha)n] the number of ways that j can be represented as a k-sum of elements of A_{k,n} is Theta(phi(n)). In this paper, we follow tradition and focus on the case phi(n)=log n, and show that a randomly selected set in an appropriate probabil"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.1808","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"}