{"paper":{"title":"Improved bound on symmetric differences of intersecting families","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lihua Feng, Qifan Wang, Yongjiang Wu","submitted_at":"2026-06-18T10:21:25Z","abstract_excerpt":"For a family $\\mathcal{F}$, it is called intersecting if $F\\cap F'\\neq \\emptyset$ for all $F,F'\\in\\mathcal{F}$.\n  We use $\\mathcal{SD}(\\mathcal{F}) = \\{F \\triangle G : F, G \\in \\mathcal{F}\\}$ to denote\n  the family of symmetric differences of $\\mathcal{F}$.\n  In 2023, Frankl, Kiselev and Kupavskii conjectured that for any intersecting family $\\mathcal{F} \\subseteq \\binom{[n]}{k}$ with $n > 10k$, the inequality $|\\mathcal{SD}(\\mathcal{F})| \\le \\sum_{\\ell=0}^{k-1} \\binom{n-1}{2\\ell}$ holds. They further observed that a proof for the range $n>3k^2$ could likely be obtained via arguments similar t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.20043","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.20043/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"}