{"paper":{"title":"From flag complexes to banner complexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Isabella Novik, Steven Klee","submitted_at":"2012-10-04T05:10:56Z","abstract_excerpt":"A notion of an $i$-banner simplicial complex is introduced. For various values of $i$, these complexes interpolate between the class of flag complexes and the class of all simplicial complexes. Examples of simplicial spheres of an arbitrary dimension that are $(i+1)$-banner but not $i$-banner are constructed. It is shown that several theorems for flag complexes have appropriate $i$-banner analogues. Among them are (1) the codimension-$(i+j-1)$ skeleton of an $i$-banner homology sphere $\\Delta$ is $2(i+j)$-Cohen--Macaulay for all $0\\leq j\\leq \\dim\\Delta+1-i$, and (2) for every $i$-banner simpli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.1297","kind":"arxiv","version":1},"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"}