{"paper":{"title":"On dihedral flows in embedded graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bart Litjens","submitted_at":"2017-09-19T14:52:44Z","abstract_excerpt":"Let $\\Gamma$ be a multigraph with for each vertex a cyclic order of the edges incident with it. For $n \\geq 3$, let $D_{2n}$ be the dihedral group of order $2n$. Define $\\mathbb{D} := \\{(\\begin{smallmatrix} 1 & a \\\\ 0 & 1 \\end{smallmatrix}) \\mid a \\in \\mathbb{Z}\\}$. In [5] it was asked whether $\\Gamma$ admits a nowhere-identity $D_{2n}$-flow if and only if it admits a nowhere-identity $\\mathbb{D}$-flow with $|a| < n$ (a `nowhere-identity $\\mathbb{D}_n$-flow'). We give counterexamples to this statement and provide general obstructions. Furthermore, the complexity of the existence of nowhere-ide"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.06469","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"}