{"?xml":{"@version":"1.0"},"edm:RDF":{"@xmlns:dc":"http://purl.org/dc/elements/1.1/","@xmlns:edm":"http://www.europeana.eu/schemas/edm/","@xmlns:wgs84_pos":"http://www.w3.org/2003/01/geo/wgs84_pos","@xmlns:foaf":"http://xmlns.com/foaf/0.1/","@xmlns:rdaGr2":"http://rdvocab.info/ElementsGr2","@xmlns:oai":"http://www.openarchives.org/OAI/2.0/","@xmlns:owl":"http://www.w3.org/2002/07/owl#","@xmlns:rdf":"http://www.w3.org/1999/02/22-rdf-syntax-ns#","@xmlns:ore":"http://www.openarchives.org/ore/terms/","@xmlns:skos":"http://www.w3.org/2004/02/skos/core#","@xmlns:dcterms":"http://purl.org/dc/terms/","edm:WebResource":[{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-QLFV3MQ0/dfbd1b79-73d7-4729-a5bd-aedbbcc9d3ec/PDF","dcterms:extent":"595 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-QLFV3MQ0/745e51e2-395f-44d1-9d09-e2685d3151c5/TEXT","dcterms:extent":"42 KB"}],"edm:TimeSpan":{"@rdf:about":"2008-2025","edm:begin":{"@xml:lang":"en","#text":"2008"},"edm:end":{"@xml:lang":"en","#text":"2025"}},"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:DOC-QLFV3MQ0","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2020","dc:creator":["Long, Shude","Ren, Han"],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:18"},{"@xml:lang":"sl","#text":"str. 51-71"}],"dc:identifier":["ISSN:1855-3966","COBISSID_HOST:38960131","URN:URN:NBN:SI:doc-QLFV3MQ0"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije"},"dc:subject":[{"@xml:lang":"en","#text":"(rooted) near-4-regular map"},{"@xml:lang":"sl","#text":"(ukoreninjen) skoraj-4-regularen zemljevid"},{"@xml:lang":"sl","#text":"asimptotika"},{"@xml:lang":"en","#text":"asymptotic"},{"@xml:lang":"en","#text":"enumerating function"},{"@xml:lang":"sl","#text":"Lagrangeova inverzija"},{"@xml:lang":"en","#text":"Lagrangian inversion"},{"@xml:lang":"sl","#text":"ločevalni cikel"},{"@xml:lang":"sl","#text":"preštevalna funkcija"},{"@xml:lang":"en","#text":"separating cycle"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"4-edge-connected 4-regular maps on the projective plane|"},"dc:description":[{"@xml:lang":"sl","#text":"In this paper rooted (near-)4-regular maps on the projective plane are investigated with respect to the root-valency, the number of edges, the number of inner faces, the number of nonroot-vertex-loops and the number of separating cycles. In particular, 4-edge connected 4-regular maps (which are related to the 3-flow conjecture by Tutte) are handled. Formulae of several types of rooted 4-edge-connected 4-regular maps on the projective plane are presented. Several known results on the number of 4-regular maps on the projective plane are also derived. Finally, using Darboux's method, a nice asymptotic formula for the numbers of this type of maps is given which implies that almost every (loopless) 4-regular map on the projective plane has a separating cycle"},{"@xml:lang":"sl","#text":"V članku raziskujemo ukoreninjene (skoraj-)4-regularne zemljevide na projektivni ravnini glede na njihovo korensko valenco, število povezav, število notranjih lic, število nekorenskih vozliščnih zank in število ločevalnih ciklov. Še posebej obravnavamo 4-povezavno povezane 4-regularne zemljevide (ki so povezani s Tutteovo domnevo o 3-toku). Predstavimo formule za več vrst ukoreninjenih 4-povezavno povezanih 4-regularnih zemljevidov na projektivni ravnini. Izpeljemo tudi več znanih rezultatov glede števila 4-regularnih zemljevidov na projektivni ravnini. Nazadnje dobimo, s pomočjo Darbouxjeve metode, za število te vrste zemljevidov lepo asimptotsko formulo, iz katere sledi, da ima skoraj vsak (brezzančni) 4-regularen zemljevid na projektivni ravnini ločevalni cikel"}],"edm:type":"TEXT","dc:type":[{"@xml:lang":"sl","#text":"znanstveno časopisje"},{"@xml:lang":"en","#text":"journals"},{"@rdf:resource":"http://www.wikidata.org/entity/Q361785"}]},"ore:Aggregation":{"@rdf:about":"http://www.dlib.si/?URN=URN:NBN:SI:DOC-QLFV3MQ0","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:DOC-QLFV3MQ0"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:DOC-QLFV3MQ0/dfbd1b79-73d7-4729-a5bd-aedbbcc9d3ec/PDF"},"edm:rights":{"@rdf:resource":"http://creativecommons.org/licenses/by/4.0/"},"edm:provider":"Slovenian National E-content Aggregator","edm:intermediateProvider":{"@xml:lang":"en","#text":"National and University Library of Slovenia"},"edm:dataProvider":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije"},"edm:object":{"@rdf:resource":"http://www.dlib.si/streamdb/URN:NBN:SI:DOC-QLFV3MQ0/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:DOC-QLFV3MQ0"}}}}