{"paper":{"title":"Cyclopermutohedron","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.MG","authors_text":"Gaiane Panina","submitted_at":"2014-01-29T11:47:11Z","abstract_excerpt":"It is known that the $k$-faces of the permutohedron $\\Pi_n$ are labeled by (all possible) linearly ordered partitions of the set $[n]=\\{1,...,n\\}$ into $(n-k)$ non-empty parts. The incidence relation corresponds to the refinement: a face $F$ contains a face $F'$ whenever the label of $F'$ refines the label of $F$. In the paper we consider the cell complex ${CP}$ defined in analogous way, replacing linear ordering by cyclic ordering. Namely, $k$-cells of the complex ${CP}$ are labeled by (all possible) cyclically ordered partitions of the set $[n+1]=\\{1,...,n, n+1\\}$ into $(n+1-k)$ non-empty pa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.7476","kind":"arxiv","version":3},"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"}