{"paper":{"title":"On maximal weakly separated set-systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Alexander V. Karzanov, Gleb A. Koshevoy, Vladimir I. Danilov","submitted_at":"2009-09-08T08:33:59Z","abstract_excerpt":"For a permutation $\\omega\\in S_n$, Leclerc and Zelevinsky \\cite{LZ} introduced a concept of $\\omega$-{\\em chamber weakly separated collection} of subsets of $\\{1,2,...,n\\}$ and conjectured that all inclusion-wise maximal collections of this sort have the same cardinality $\\ell(\\omega)+n+1$, where $\\ell(\\omega)$ is the length of $\\omega$. We answer affirmatively this conjecture and present a generalization and additional results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.1423","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"}