{"paper":{"title":"Deviation probabilities for arithmetic progressions and other regular discrete structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT","math.PR"],"primary_cat":"math.CO","authors_text":"Gonzalo Fiz Pontiveros, Matheus Secco, Oriol Serra, Simon Griffiths","submitted_at":"2019-10-28T17:46:20Z","abstract_excerpt":"Let the random variable $X\\, :=\\, e(\\mathcal{H}[B])$ count the number of edges of a hypergraph $\\mathcal{H}$ induced by a random $m$ element subset $B$ of its vertex set. Focussing on the case that $\\mathcal{H}$ satisfies some regularity condition we prove bounds on the probability that $X$ is far from its mean. It is possible to apply these results to discrete structures such as the set of $k$-term arithmetic progressions in the cyclic group $\\mathbb{Z}_N$. Furthermore, we show that our main theorem is essentially best possible and we deduce results for the case $B\\sim B_p$ is generated by in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.12835","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/1910.12835/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"}