{"paper":{"title":"Almost simplicial polytopes I. The lower and upper bound theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"David Yost, Eran Nevo, Guillermo Pineda-Villavicencio, Julien Ugon","submitted_at":"2015-10-28T11:22:12Z","abstract_excerpt":"We study $n$-vertex $d$-dimensional polytopes with at most one nonsimplex facet with, say, $d+s$ vertices, called {\\it almost simplicial polytopes}. We provide tight lower and upper bound theorems for these polytopes as functions of $d,n$ and $s$, thus generalizing the classical Lower Bound Theorem by Barnette and Upper Bound Theorem by McMullen, which treat the case of $s=0$. We characterize the minimizers and provide examples of maximizers, for any $d$. Our construction of maximizers is a generalization of cyclic polytopes, based on a suitable variation of the moment curve, and is of indepen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08258","kind":"arxiv","version":3},"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"}