{"paper":{"title":"On diamond-free subposets of the Boolean lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lucas Kramer, Michael Young, Ryan R. Martin","submitted_at":"2012-05-07T19:57:56Z","abstract_excerpt":"The Boolean lattice of dimension two, also known as the diamond, consists of four distinct elements with the following property: $A\\subset B,C\\subset D$. A diamond-free family in the $n$-dimensional Boolean lattice is a subposet such that no four elements form a diamond. Note that elements $B$ and $C$ may or may not be related.\n  There is a diamond-free family in the $n$-dimensional Boolean lattice of size $(2-o(1)){n\\choose\\lfloor n/2\\rfloor}$. In this paper, we prove that any diamond-free family in the $n$-dimensional Boolean lattice has size at most $(2.25+o(1)){n\\choose\\lfloor n/2\\rfloor}$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1501","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":""},"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"}