{"paper":{"title":"On Uniform f-vectors of Cutsets 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, Shahriar Shahriari","submitted_at":"2015-12-09T18:11:38Z","abstract_excerpt":"Let $[n] = \\{1, 2, \\ldots, n\\}$ and let $2^{[n]}$ be the collection of all subsets of $[n]$ ordered by inclusion. ${\\cal C} \\subseteq 2^{[n]}$ is a {\\em cutset} if it meets every maximal chain in $2^{[n]}$, and the {\\em width} of ${\\cal C} \\subseteq 2^{[n]}$ is the minimum number of chains in a chain decomposition of ${\\cal C}$. Fix $0 \\leq m \\leq l \\leq n$. What is the smallest value of $k$ such that there exists a cutset that consists only of subsets of sizes between $m$ and $l$, and such that it contains exactly $k$ subsets of size $i$ for each $m \\leq i \\leq l$? The answer, which we denote"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02973","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"}