{"paper":{"title":"Triangulations of $\\mathbb{RP}^n$ with few vertices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Soumen Sarkar","submitted_at":"2014-03-02T01:14:33Z","abstract_excerpt":"P. Arnoux and A. Marin showed that any triangulation of $\\mathbb{RP}^n$ contains more than $\\frac{(n+1)(n+2)}{2}$ vertices if $n \\geq 3$. We construct some natural triangulation of $\\mathbb{RP}^n$ with $\\frac{n(n+5)}{2}-1$ vertices for all $n \\geq 3$. Previously, it was known that $\\mathbb{RP}^n$ has $\\mathbb{Z}_2^n$-equivariant triangulation with $n(n+1)$ vertices for $n \\geq 6$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0146","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"}