{"paper":{"title":"On chromatic indices of finite affine spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Adri\\'an V\\'azquez-\\'Avila, Christian Rubio-Montiel, Gabriela Araujo-Pardo, Gy\\\"orgy Kiss","submitted_at":"2017-11-24T16:05:10Z","abstract_excerpt":"The pseudoachromatic index of the finite affine space $\\mathrm{AG}(n,q),$ denoted by $\\psi'(\\mathrm{AG}(n,q)),$ is the the maximum number of colors in any complete line-coloring of $\\mathrm{AG}(n,q).$ When the coloring is also proper, the maximum number of colors is called the achromatic index of $\\mathrm{AG}(n,q).$ We prove that if $n$ is even then $\\psi'(\\mathrm{AG}(n,q))\\sim q^{1.5n-1}$; while when $n$ is odd the value is bounded by $q^{1.5(n-1)}<\\psi'(\\mathrm{AG}(n,q))<q^{1.5n-1}$. Moreover, we prove that the achromatic index of $\\mathrm{AG}(n,q)$ is $q^{1.5n-1}$ for even $n,$ and we provi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.09031","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"}