{"paper":{"title":"Improved bounds for induced poset saturation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Heather C. Smith, Ryan R. Martin, Shanise Walker","submitted_at":"2019-08-03T02:27:31Z","abstract_excerpt":"Given a finite poset $\\mathcal{P}$, a family $\\mathcal{F}$ of elements in the Boolean lattice is induced-$\\mathcal{P}$-saturated if $\\mathcal{F}$ contains no copy of $\\mathcal{P}$ as an induced subposet but every proper superset of $\\mathcal{F}$ contains a copy of $\\mathcal{P}$ as an induced subposet. The minimum size of an induced-$\\mathcal{P}$-saturated family in the $n$-dimensional Boolean lattice, denoted $\\operatorname{sat}^*(n,\\mathcal{P})$, was first studied by Ferrara et al. (2017).\n  Our work focuses on strengthening lower bounds. For the 4-point poset known as the diamond, we prove $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.01108","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/1908.01108/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"}