Matches in SemOpenAlex for { <https://semopenalex.org/work/W4302279167> ?p ?o ?g. }
Showing items 1 to 53 of
53
with 100 items per page.
- W4302279167 abstract "Baker and Wang define the so-called Bernardi action of the sandpile group of a ribbon graph on the set of its spanning trees. This potentially depends on a fixed vertex of the graph but it is independent of the base vertex if and only if the ribbon structure is planar, moreover, in this case the Bernardi action is compatible with planar duality. Earlier, Chan, Church and Grochow and Chan, Glass, Macauley, Perkinson, Werner and Yang proved analogous results about the rotor-routing action. Baker and Wang moreover showed that the Bernardi and rotor-routing actions coincide for plane graphs. We clarify this still confounding picture by giving a canonical definition for the planar Bernardi/rotor-routing action, and also a canonical isomorphism between sandpile groups of planar dual graphs. Our canonical definition implies the compatibility with planar duality via an extremely short argument. We also show hidden symmetries of the problem by proving our results in the slightly more general setting of balanced plane digraphs. Any balanced plane digraph gives rise to a trinity, i.e., a triangulation of the sphere with a three-coloring of the $0$-simplices. Our most important tool is a group associated to trinities, introduced by Cavenagh and Wanless, and a result of a subset of the authors characterizing the Bernardi bijection in terms of a dissection of a root polytope." @default.
- W4302279167 created "2022-10-06" @default.
- W4302279167 creator A5000253602 @default.
- W4302279167 creator A5060945252 @default.
- W4302279167 creator A5068101962 @default.
- W4302279167 date "2019-05-05" @default.
- W4302279167 modified "2023-10-06" @default.
- W4302279167 title "The sandpile group of a trinity and a canonical definition for the planar Bernardi action" @default.
- W4302279167 doi "https://doi.org/10.48550/arxiv.1905.01689" @default.
- W4302279167 hasPublicationYear "2019" @default.
- W4302279167 type Work @default.
- W4302279167 citedByCount "0" @default.
- W4302279167 crossrefType "posted-content" @default.
- W4302279167 hasAuthorship W4302279167A5000253602 @default.
- W4302279167 hasAuthorship W4302279167A5060945252 @default.
- W4302279167 hasAuthorship W4302279167A5068101962 @default.
- W4302279167 hasBestOaLocation W43022791671 @default.
- W4302279167 hasConcept C101837359 @default.
- W4302279167 hasConcept C105313907 @default.
- W4302279167 hasConcept C114614502 @default.
- W4302279167 hasConcept C118615104 @default.
- W4302279167 hasConcept C132525143 @default.
- W4302279167 hasConcept C2524010 @default.
- W4302279167 hasConcept C2779145032 @default.
- W4302279167 hasConcept C33923547 @default.
- W4302279167 hasConcept C80899671 @default.
- W4302279167 hasConcept C96469262 @default.
- W4302279167 hasConceptScore W4302279167C101837359 @default.
- W4302279167 hasConceptScore W4302279167C105313907 @default.
- W4302279167 hasConceptScore W4302279167C114614502 @default.
- W4302279167 hasConceptScore W4302279167C118615104 @default.
- W4302279167 hasConceptScore W4302279167C132525143 @default.
- W4302279167 hasConceptScore W4302279167C2524010 @default.
- W4302279167 hasConceptScore W4302279167C2779145032 @default.
- W4302279167 hasConceptScore W4302279167C33923547 @default.
- W4302279167 hasConceptScore W4302279167C80899671 @default.
- W4302279167 hasConceptScore W4302279167C96469262 @default.
- W4302279167 hasLocation W43022791671 @default.
- W4302279167 hasOpenAccess W4302279167 @default.
- W4302279167 hasPrimaryLocation W43022791671 @default.
- W4302279167 hasRelatedWork W1964289883 @default.
- W4302279167 hasRelatedWork W2036118949 @default.
- W4302279167 hasRelatedWork W2047600543 @default.
- W4302279167 hasRelatedWork W2082494488 @default.
- W4302279167 hasRelatedWork W2159377379 @default.
- W4302279167 hasRelatedWork W2998116189 @default.
- W4302279167 hasRelatedWork W3001481731 @default.
- W4302279167 hasRelatedWork W3194176857 @default.
- W4302279167 hasRelatedWork W4206244388 @default.
- W4302279167 hasRelatedWork W4210490117 @default.
- W4302279167 isParatext "false" @default.
- W4302279167 isRetracted "false" @default.
- W4302279167 workType "article" @default.