{"paper":{"title":"On the generalized lower bound conjecture for polytopes and spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.CO","authors_text":"Eran Nevo, Satoshi Murai","submitted_at":"2012-03-08T09:46:30Z","abstract_excerpt":"In 1971, McMullen and Walkup posed the following conjecture, which is called the generalized lower bound conjecture: If $P$ is a simplicial $d$-polytope then its $h$-vector $(h_0,h_1,...,h_d)$ satisfies $h_0 \\leq h_1 \\leq ... \\leq h_{\\lfloor \\frac d 2 \\rfloor}$. Moreover, if $h_{r-1}=h_r$ for some $r \\leq \\frac d 2$ then $P$ can be triangulated without introducing simplices of dimension $\\leq d-r$.\n  The first part of the conjecture was solved by Stanley in 1980 using the hard Lefschetz theorem for projective toric varieties. In this paper, we give a proof of the remaining part of the conjectu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.1720","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"}