{"paper":{"title":"Variations on the Bollob\\'as set-pair theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"G\\'abor Heged\\\"us, P\\'eter Frankl","submitted_at":"2023-07-27T08:51:50Z","abstract_excerpt":"Let $X$ be an $n$-element set. A set-pair system $\\mbox{$\\cal P$}=\\{(A_i,B_i)\\}_{1\\leq i\\leq m}$ is a collection of pairs of disjoint subsets of $X$. It is called skew Bollob\\'as system if $A_i\\cap B_j\\neq \\emptyset$ for all $1\\leq i<j \\leq m$. The best possible inequality $$ \\sum_{i=1}^m \\frac{1}{{|A_i|+|B_i| \\choose |A_i|}}\\leq n+1. $$ is established along with some more results of similar flavor."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.14704","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/2307.14704/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"}