{"paper":{"title":"On $k$-stellated and $k$-stacked spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GT","authors_text":"Basudeb Datta, Bhaskar Bagchi","submitted_at":"2012-08-07T10:20:22Z","abstract_excerpt":"We introduce the class $\\Sigma_k(d)$ of $k$-stellated (combinatorial) spheres of dimension $d$ ($0 \\leq k \\leq d + 1$) and compare and contrast it with the class ${\\cal S}_k(d)$ ($0 \\leq k \\leq d$) of $k$-stacked homology $d$-spheres. We have $\\Sigma_1(d) = {\\cal S}_1(d)$, and $\\Sigma_k(d) \\subseteq {\\cal S}_k(d)$ for $d \\geq 2k - 1$. However, for each $k \\geq 2$ there are $k$-stacked spheres which are not $k$-stellated. The existence of $k$-stellated spheres which are not $k$-stacked remains an open question.\n  We also consider the class ${\\cal W}_k(d)$ (and ${\\cal K}_k(d)$) of simplicial com"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1389","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"}