{"paper":{"title":"Bipartite-uniform hypermaps on the sphere","license":"","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Antonio Breda d'Azevedo, Rui Duarte","submitted_at":"2006-07-12T09:14:46Z","abstract_excerpt":"A hypermap is (hypervertex-) bipartite if its hypervertices can be 2-coloured in such a way that ``neighbouring'' hypervertices have different colours. It is bipartite-uniform if within each of the sets of hypervertices of the same colour, hyperedges and hyperfaces, elements have common valencies. The flags of a bipartite hypermap are naturally 2-coloured by assigning the colour of its adjacent hypervertices. A hypermap is bipartite-regular if the automorphism group acts transitively on each set of coloured flags. If the automorphism group acts transitively on the set of all flags, the hyperma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0607281","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"}