{"paper":{"title":"On stellated spheres, shellable balls, lower bounds and a combinatorial criterion for tightness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Basudeb Datta, Bhaskar Bagchi","submitted_at":"2011-02-04T09:17:44Z","abstract_excerpt":"We introduce the $k$-stellated spheres and compare and contrast them with $k$-stacked spheres. It is shown that for $d \\geq 2k$, any $k$-stellated sphere of dimension $d$ bounds a unique and canonically defined $k$-stacked ball. In parallel, any $k$-stacked polytopal sphere of dimension $d\\geq 2k$ bounds a unique and canonically defined $k$-stacked ball. We consider the class ${\\cal W}_k(d)$ of combinatorial $d$-manifolds with $k$-stellated links. For $d\\geq 2k+2$, any member of ${\\cal W}_k(d)$ bounds a unique and canonically defined \"$k$-stacked\" $(d+1)$-manifold.\n  We introduce the mu-vector"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.0856","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"}