{"paper":{"title":"The combinatorics of interval-vector polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Amanda Ruiz, Gabriel Dorfsman-Hopkins, Jessica De Silva, Joseph Pruitt, Matthias Beck","submitted_at":"2012-11-09T04:29:34Z","abstract_excerpt":"An \\emph{interval vector} is a $(0,1)$-vector in $\\mathbb{R}^n$ for which all the 1's appear consecutively, and an \\emph{interval-vector polytope} is the convex hull of a set of interval vectors in $\\mathbb{R}^n$. We study three particular classes of interval vector polytopes which exhibit interesting geometric-combinatorial structures; e.g., one class has volumes equal to the Catalan numbers, whereas another class has face numbers given by the Pascal 3-triangle."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.2039","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"}