{"paper":{"title":"Small Sets with Large Difference Sets","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Luka Milicevic","submitted_at":"2017-05-24T13:46:11Z","abstract_excerpt":"For every $\\epsilon > 0$ and $k \\in \\mathbb{N}$, Haight constructed a set $A \\subset \\mathbb{Z}_N$ ($\\mathbb{Z}_N$ stands for the integers modulo $N$) for a suitable $N$, such that $A-A = \\mathbb{Z}_N$ and $|kA| < \\epsilon N$. Recently, Nathanson posed the problem of constructing sets $A \\subset \\mathbb{Z}_N$ for given polynomials $p$ and $q$, such that $p(A) = \\mathbb{Z}_N$ and $|q(A)| < \\epsilon N$, where $p(A)$ is the set $\\{p(a_1, a_2, \\dots, a_n)\\phantom{.}\\colon\\phantom{.}a_1, a_2, \\dots, a_n \\in A\\}$, when $p$ has $n$ variables. In this paper, we give a partial answer to Nathanson's que"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.08760","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"}