FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2158909663> ?p ?o ?g. }

• W2158909663 abstract "A map is an embedding of the vertices and edges of a graph into a compact 2manifold such that the remainder of the surface has components homeomorphic to open disks. With the goal of proving the Four Colour Theorem, Tutte began the field of map enumeration in the 1960’s. His methods included developing the edge deletion decomposition, developing and solving a recurrence and functional equation based on this decomposition, and developing the medial bijection between two equinumerous infinite families of maps. Beginning in the 1980’s Jackson, Goulden and Visentin applied algebraic methods in enumeration of non-planar and non-orientable maps, to obtain results of interest for mathematical physics and algebraic geometry, and the Quadrangulation Conjecture and the Map-Jack Conjecture. A special case of the former is solved by Tutte’s medial bijection. The latter uses Jack symmetric functions which are a topic of active research. In the 1960’s Walsh and Lehman introduced a method of encoding orientable maps. We develop a similar method, based on depth first search and extended to non-orientable maps. With this, we develop a bijection that extends Tutte’s medial bijection and partially solves the Quadrangulation Conjecture. Walsh extended Tutte’s recurrence for planar maps to a recurrence for all orientable maps. We further extend the recurrence to include non-orientable maps, and express it as a partial differential equation satisfied by the generating series. By appropriately interpolating the differential equation and applying the depth first search method, we construct a parameter that empirically fulfils the conditions of the Map-Jack Conjecture, and we prove some of its predicted properties. Arques and Beraud recently obtained a continued fraction form of a specialisation of the generating series for maps. We apply the depth search method with an ordinary differential equation, to construct a bijection whose existence is implied by the continued fraction." @default.
• W2158909663 created "2016-06-24" @default.
• W2158909663 creator A5003985977 @default.
• W2158909663 date "2000-01-01" @default.
• W2158909663 modified "2023-09-28" @default.
• W2158909663 title "Differential Equations and Depth First Search for Enumeration of Maps in Surfaces" @default.
• W2158909663 cites W1497051802 @default.
• W2158909663 cites W1558273801 @default.
• W2158909663 cites W1656838262 @default.
• W2158909663 cites W1806580154 @default.
• W2158909663 cites W1831033967 @default.
• W2158909663 cites W1971175983 @default.
• W2158909663 cites W2005300808 @default.
• W2158909663 cites W2007152918 @default.
• W2158909663 cites W2012632087 @default.
• W2158909663 cites W2016084340 @default.
• W2158909663 cites W2016710045 @default.
• W2158909663 cites W2021355739 @default.
• W2158909663 cites W2021646443 @default.
• W2158909663 cites W2033980874 @default.
• W2158909663 cites W2034573815 @default.
• W2158909663 cites W2042456974 @default.
• W2158909663 cites W2061180434 @default.
• W2158909663 cites W2064797648 @default.
• W2158909663 cites W2065211664 @default.
• W2158909663 cites W2066624456 @default.
• W2158909663 cites W2069422812 @default.
• W2158909663 cites W2077030884 @default.
• W2158909663 cites W2124818311 @default.
• W2158909663 cites W2134984950 @default.
• W2158909663 cites W2148260769 @default.
• W2158909663 cites W2320988437 @default.
• W2158909663 cites W2331875213 @default.
• W2158909663 cites W2495029002 @default.
• W2158909663 cites W2799004609 @default.
• W2158909663 cites W3163477145 @default.
• W2158909663 cites W72097083 @default.
• W2158909663 hasPublicationYear "2000" @default.
• W2158909663 type Work @default.
• W2158909663 sameAs 2158909663 @default.
• W2158909663 citedByCount "1" @default.
• W2158909663 crossrefType "dissertation" @default.
• W2158909663 hasAuthorship W2158909663A5003985977 @default.
• W2158909663 hasConcept C101837359 @default.
• W2158909663 hasConcept C114614502 @default.
• W2158909663 hasConcept C118615104 @default.
• W2158909663 hasConcept C132525143 @default.
• W2158909663 hasConcept C156340839 @default.
• W2158909663 hasConcept C24424167 @default.
• W2158909663 hasConcept C2780990831 @default.
• W2158909663 hasConcept C33923547 @default.
• W2158909663 hasConceptScore W2158909663C101837359 @default.
• W2158909663 hasConceptScore W2158909663C114614502 @default.
• W2158909663 hasConceptScore W2158909663C118615104 @default.
• W2158909663 hasConceptScore W2158909663C132525143 @default.
• W2158909663 hasConceptScore W2158909663C156340839 @default.
• W2158909663 hasConceptScore W2158909663C24424167 @default.
• W2158909663 hasConceptScore W2158909663C2780990831 @default.
• W2158909663 hasConceptScore W2158909663C33923547 @default.
• W2158909663 hasLocation W21589096631 @default.
• W2158909663 hasOpenAccess W2158909663 @default.
• W2158909663 hasPrimaryLocation W21589096631 @default.
• W2158909663 hasRelatedWork W1530585715 @default.
• W2158909663 hasRelatedWork W2062669074 @default.
• W2158909663 hasRelatedWork W2963983543 @default.
• W2158909663 hasRelatedWork W3107978990 @default.
• W2158909663 hasRelatedWork W3124053918 @default.
• W2158909663 hasRelatedWork W626905740 @default.
• W2158909663 hasRelatedWork W2738648802 @default.
• W2158909663 hasRelatedWork W2896649814 @default.
• W2158909663 hasRelatedWork W2944729808 @default.
• W2158909663 hasRelatedWork W627820511 @default.
• W2158909663 isParatext "false" @default.
• W2158909663 isRetracted "false" @default.
• W2158909663 magId "2158909663" @default.
• W2158909663 workType "dissertation" @default.