{"paper":{"title":"On the Minimum Width of a Cutset in the Truncated Boolean Lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"B\\'ela Bajnok","submitted_at":"2015-12-09T18:22:37Z","abstract_excerpt":"For integers $0 \\leq m \\leq l \\leq n-m$, the truncated Boolean lattice ${\\cal B}_n(m,l)$ is the poset of all subsets of $[n] = \\{1, 2, \\ldots, n\\}$ which have size at least $m$ and at most $l$. ${\\cal C} \\subseteq {\\cal B}_n(m,l)$ is a {\\em cutset} if it meets every chain of length $l-m$ in ${\\cal B}_n(m,l)$, and the {\\em width} of ${\\cal C}$ is the size of the largest antichain in ${\\cal C}$. We conjecture that for $n >> m$ the minimum width $h_n(m,l)$ of a cutset in ${\\cal B}_n(m,l)$ is $\\Sigma_{j \\geq 0} \\Delta_n(m-jc) = \\Delta_n(m)+\\Delta_n(m-c)+\\Delta_n(m-2c)+ \\dots$, where $c=l-m+1$ is t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02978","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":""},"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"}