{"paper":{"title":"Arc Transitive Maps with underlying Rose Window Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alejandra Ramos-Rivera, Isabel Hubard, Primo\\v{z} \\v{S}parl","submitted_at":"2017-08-03T12:21:05Z","abstract_excerpt":"Let ${\\cal M}$ be a map with the underlying graph $\\Gamma$. The automorphism group $Aut({\\cal M})$ induces a natural action on the set of all vertex-edge-face incident triples, called {\\em flags} of ${\\cal M}$. The map ${\\cal M}$ is said to be a {\\em $k$-orbit} map if $Aut({\\cal M})$ has $k$ orbits on the set of all flags of ${\\cal M}$. It is known that there are seven different classes of $2$-orbit maps, with only four of them corresponding to arc-transitive maps, that is maps for which $Aut{\\cal M}$ acts arc-transitively on the underlying graph $\\Gamma$. The Petrie dual operator links these "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.01112","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"}