{"paper":{"title":"Volume and lattice points counting for the cyclopermutohedron","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Gaiane Panina, Ilya Nekrasov","submitted_at":"2015-05-02T16:37:40Z","abstract_excerpt":"The face lattice of the permutohedron realizes the combinatorics of linearly ordered partitions of the set $[n]=\\{1,...,n\\}$. Similarly, the cyclopermutohedron is a virtual polytope that realizes the combinatorics of cyclically ordered partitions of $[n]$.\n  It is known that the volume of the standard permutohedron equals the number of trees with $n$ labeled vertices multiplied by $\\sqrt{n}$. The number of integer points of the standard permutohedron equals the number of forests on $n$ labeled vertices.\n  In the paper we prove that the volume of the cyclopermutohedron also equals some weighted"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00352","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"}