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- Rotation_system abstract "In combinatorial mathematics, rotation systems encode embeddings of graphs onto orientable surfaces, by describing the circular ordering of a graph's edges around each vertex.A more formal definition of a rotation system involves pairs of permutations; such a pair is sufficient to determine a multigraph, a surface, and a 2-cell embedding of the multigraph onto the surface.Every rotation scheme defines a unique 2-cell embedding of a connected multigraph on a closed oriented surface (up to orientation preserving topological equivalence). Conversely, any embedding of a connected multigraph G on an oriented closed surface defines a unique rotation system having G as its underlying multigraph. This fundamental equivalence between rotation systems and 2-cell-embeddings was first settled in a dual form by Heffter and extensively used by Ringel during the 1950s. Independently, Edmonds gave the primal form of the theorem and the details of his study have been popularized by Youngs. The generalization to the whole set of multigraphs was developed by Gross and Alpert.Rotation systems are related to, but not the same as, the rotation maps used by Reingold et al. (2002) to define the zig-zag product of graphs. A rotation system specifies a circular ordering of the edges around each vertex, while a rotation map specifies a (non-circular) permutation of the edges at each vertex. In addition, rotation systems can be defined for any graph, while as Reingold et al. define them rotation maps are restricted to regular graphs.".
- Rotation_system wikiPageID "3118411".
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- Rotation_system wikiPageRevisionID "627081190".
- Rotation_system wikiPageWikiLink Annals_of_Mathematics.
- Rotation_system wikiPageWikiLink Bojan_Mohar.
- Rotation_system wikiPageWikiLink Carsten_Thomassen.
- Rotation_system wikiPageWikiLink Category:Topological_graph_theory.
- Rotation_system wikiPageWikiLink Circular_ordering.
- Rotation_system wikiPageWikiLink Combinatorics.
- Rotation_system wikiPageWikiLink Cyclic_order.
- Rotation_system wikiPageWikiLink Euler_formula.
- Rotation_system wikiPageWikiLink Eulers_formula.
- Rotation_system wikiPageWikiLink Generating_set_of_a_group.
- Rotation_system wikiPageWikiLink Genus_(mathematics).
- Rotation_system wikiPageWikiLink Gerhard_Ringel.
- Rotation_system wikiPageWikiLink Graph_embedding.
- Rotation_system wikiPageWikiLink Graph_theory.
- Rotation_system wikiPageWikiLink Group_(mathematics).
- Rotation_system wikiPageWikiLink Group_action.
- Rotation_system wikiPageWikiLink Indiana_University_Mathematics_Journal.
- Rotation_system wikiPageWikiLink Involution_(mathematics).
- Rotation_system wikiPageWikiLink Jack_Edmonds.
- Rotation_system wikiPageWikiLink Journal_of_Mathematics_and_Mechanics.
- Rotation_system wikiPageWikiLink Mathematics.
- Rotation_system wikiPageWikiLink Mathematische_Annalen.
- Rotation_system wikiPageWikiLink Notices_of_the_American_Mathematical_Society.
- Rotation_system wikiPageWikiLink Orientability.
- Rotation_system wikiPageWikiLink Regular_graph.
- Rotation_system wikiPageWikiLink Rotation_map.
- Rotation_system wikiPageWikiLink Springer-Verlag.
- Rotation_system wikiPageWikiLink Springer_Science+Business_Media.
- Rotation_system wikiPageWikiLink Surface.
- Rotation_system wikiPageWikiLink Zig-zag_product.
- Rotation_system wikiPageWikiLinkText "Rotation system".
- Rotation_system wikiPageWikiLinkText "rotation system".
- Rotation_system hasPhotoCollection Rotation_system.
- Rotation_system wikiPageUsesTemplate Template:Cite_book.
- Rotation_system wikiPageUsesTemplate Template:Cite_journal.
- Rotation_system wikiPageUsesTemplate Template:Reflist.
- Rotation_system subject Category:Topological_graph_theory.
- Rotation_system comment "In combinatorial mathematics, rotation systems encode embeddings of graphs onto orientable surfaces, by describing the circular ordering of a graph's edges around each vertex.A more formal definition of a rotation system involves pairs of permutations; such a pair is sufficient to determine a multigraph, a surface, and a 2-cell embedding of the multigraph onto the surface.Every rotation scheme defines a unique 2-cell embedding of a connected multigraph on a closed oriented surface (up to orientation preserving topological equivalence). ".
- Rotation_system label "Rotation system".
- Rotation_system sameAs m.08smn0.
- Rotation_system sameAs Q7370316.
- Rotation_system sameAs Q7370316.
- Rotation_system wasDerivedFrom Rotation_system?oldid=627081190.
- Rotation_system isPrimaryTopicOf Rotation_system.