{"paper":{"title":"Illumination of convex bodies with many symmetries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Konstantin Tikhomirov","submitted_at":"2016-06-29T06:47:18Z","abstract_excerpt":"Let $n\\geq C$ for a large universal constant $C>0$, and let $B$ be a convex body in $R^n$ such that for any $(x_1,x_2,\\dots,x_n)\\in B$, any choice of signs $\\varepsilon_1,\\varepsilon_2,\\dots,\\varepsilon_n\\in\\{-1,1\\}$ and for any permutation $\\sigma$ on $n$ elements we have $(\\varepsilon_1x_{\\sigma(1)},\\varepsilon_2x_{\\sigma(2)},\\dots,\\varepsilon_nx_{\\sigma(n)})\\in B$. We show that if $B$ is not a cube then $B$ can be illuminated by strictly less than $2^n$ sources of light. This confirms the Hadwiger--Gohberg--Markus illumination conjecture for unit balls of $1$-symmetric norms in $R^n$ for al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.08976","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"}