{"paper":{"title":"Generalizing the Distribution of Missing Sums in Sumsets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.NT","authors_text":"Chenyang Sun, Dylan King, Hung V. Chu, Lily Shao, Noah Luntzlara, Steven J. Miller, Thomas C. Martinez, Victor Xu","submitted_at":"2020-05-16T13:11:08Z","abstract_excerpt":"Given a finite set of integers $A$, its sumset is $A+A:= \\{a_i+a_j \\mid a_i,a_j\\in A\\}$. We examine $|A+A|$ as a random variable, where $A\\subset I_n = [0,n-1]$, the set of integers from 0 to $n-1$, so that each element of $I_n$ is in $A$ with a fixed probability $p \\in (0,1)$. Recently, Martin and O'Bryant studied the case in which $p=1/2$ and found a closed form for $\\mathbb{E}[|A+A|]$. Lazarev, Miller, and O'Bryant extended the result to find a numerical estimate for $\\text{Var}(|A+A|)$ and bounds on the number of missing sums in $A+A$, $m_{n\\,;\\,p}(k) := \\mathbb{P}(2n-1-|A+A|=k)$. Their pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2005.07981","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2005.07981/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}