{"paper":{"title":"The maximum number of faces of the Minkowski sum of two convex polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.CG","authors_text":"Eleni Tzanaki, Menelaos I. Karavelas","submitted_at":"2011-06-30T14:59:45Z","abstract_excerpt":"We derive tight expressions for the maximum number of $k$-faces, $0\\le{}k\\le{}d-1$, of the Minkowski sum, $P_1\\oplus{}P_2$, of two $d$-dimensional convex polytopes $P_1$ and $P_2$, as a function of the number of vertices of the polytopes.\n  For even dimensions $d\\ge{}2$, the maximum values are attained when $P_1$ and $P_2$ are cyclic $d$-polytopes with disjoint vertex sets. For odd dimensions $d\\ge{}3$, the maximum values are attained when $P_1$ and $P_2$ are $\\lfloor\\frac{d}{2}\\rfloor$-neighborly $d$-polytopes, whose vertex sets are chosen appropriately from two distinct $d$-dimensional momen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.6254","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"}