{"paper":{"title":"Principally Box-integer Polyhedra and Equimodular Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Louis-Hadrien Robert, Patrick Chervet, Roland Grappe","submitted_at":"2018-04-24T12:10:57Z","abstract_excerpt":"A polyhedron is box-integer if its intersection with any integer box $\\{\\ell\\leq x \\leq u\\}$ is integer. We define principally box-integer polyhedra to be the polyhedra $P$ such that $kP$ is box-integer whenever $kP$ is integer. We characterize them in several ways, involving equimodular matrices and box-total dual integral (box-TDI) systems. A rational $r\\times n$ matrix is equimodular if it has full row rank and its nonzero $r\\times r$ determinants all have the same absolute value. A face-defining matrix is a full row rank matrix describing the affine hull of a face of the polyhedron. Box-TD"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.08977","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"}