{"paper":{"title":"Cubillages on cyclic zonotopes, membranes, and higher separatation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"A.V. Karzanov, G.A. Koshevoy, V.I. Danilov","submitted_at":"2018-10-12T13:53:37Z","abstract_excerpt":"We study certain structural properties of fine zonotopal tilings, or cubillages, on cyclic zonotopes $Z(n,d)$ of an arbitrary dimension $d$ and their relations to $(d-1)$-separated collections of subsets of a set $\\{1,2,\\ldots,n\\}$. (Collections of this sort are well known as strongly separated ones when $d=2$, and as chord separated ones when $d=3$.)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.05517","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"}