{"paper":{"title":"On the integer points in a lattice polytope: n-fold Minkowski sum and boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.MG","authors_text":"Marko Lindner, Steffen Roch","submitted_at":"2010-06-10T15:09:02Z","abstract_excerpt":"In this article we compare the set of integer points in the homothetic copy $n\\Pi$ of a lattice polytope $\\Pi\\subseteq\\R^d$ with the set of all sums $x_1+\\cdots+x_n$ with $x_1,...,x_n\\in \\Pi\\cap\\Z^d$ and $n\\in\\N$. We give conditions on the polytope $\\Pi$ under which these two sets coincide and we discuss two notions of boundary for subsets of $\\Z^d$ or, more generally, subsets of a finitely generated discrete group."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.2053","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1006.2053/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}