{"?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-RWRF3E4I/d5662206-4670-4753-8094-11f20d85a892/PDF","dcterms:extent":"386 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-RWRF3E4I/ef052011-d1dc-4bd7-a084-023003878bf5/TEXT","dcterms:extent":"40 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-RWRF3E4I","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2022","dc:creator":"Tyc, Adam","dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:22"},{"@xml:lang":"sl","#text":"P1.02 (str. 23-39)"}],"dc:identifier":["DOI:10.26493/1855-3974.2242.842","COBISSID_HOST:115140867","ISSN:1855-3966","URN:URN:NBN:SI:doc-RWRF3E4I"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije"},"dc:subject":[{"@xml:lang":"sl","#text":"cikcak črta"},{"@xml:lang":"en","#text":"directed Eulerian embedding"},{"@xml:lang":"sl","#text":"triangulacija ploskve"},{"@xml:lang":"en","#text":"triangulation of a surface"},{"@xml:lang":"sl","#text":"usmerjena evklidska vložitev"},{"@xml:lang":"en","#text":"zigzag"},{"@xml:lang":"sl","#text":"z-monodromija"},{"@xml:lang":"en","#text":"z-monodromy"},{"@xml:lang":"sl","#text":"z-orientacija"},{"@xml:lang":"en","#text":"z-orientation"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Z-oriented triangulations of surfaces|"},"dc:description":[{"@xml:lang":"sl","#text":"The main objects of the paper are ?$z$?-oriented triangulations of connected closed 2-dimensional surfaces. A ?$z$?-orientation of a map is a minimal collection of zigzags which double covers the set of edges. We have two possibilities for an edge -- zigzags from the ?$z$?-orientation pass through this edge in different directions (type I) or in the same direction (type II). Then there are two types of faces in a triangulation: the first type is when two edges of the face are of type I and one edge is of type II and the second type is when all edges of the face are of type II. We investigate ?$z$?-oriented triangulations with all faces of the first type (in the general case, any ?$z$?-oriented triangulation can be shredded to a ?$z$?-oriented triangulation of such type). A zigzag is homogeneous if it contains precisely two edges of type I after any edge of type II. We give a topological characterization of the homogeneity of zigzags; in particular, we describe a one-to-one correspondence between ?$z$?-oriented triangulations with homogeneous zigzags and closed 2-cell embeddings of directed Eulerian graphs in surfaces. At the end, we give an application to one type of the ?$z$?-monodromy"},{"@xml:lang":"sl","#text":"Glavni predmet članka so ?$z$?-orientirane triangulacije povezanih 2-dimenzionalnih ploskev. ?$z$?-orientacija zemljevida je minimalna kolekcija cikcak črt, ki dvojno pokriva množico povezav. Imamo dva tipa povezav – cikcak črte iz ?$z$?-orientacije potekajo skozi dano povezavo v različnih smereh (tip I) ali pa v isti smeri (tip II). V skladu s tem obstajata dva tipa lic v triangulaciji: pri prvem tipu sta dve povezavi lica tipa I, ena povezava pa tipa II, pri drugem tipu pa so vse povezave lica tipa II. Preučujemo ?$z$?-orientirane triangulacije z vsemi lici prvega tipa (v splošnem primeru velja, da se da poljubna ?$z$?-orientirana triangulacija razrezati na ?$z$?-orientirano triangulacijo tega tipa). Cikcak črta je homogena, če vsaki povezavi tipa II sledita natanko dve povezavi tipa I. Podamo topološko karakterizacijo homogenosti cikcak črt; posebej, opišemo bijektivno korespondenco med z-orientiranimi triangulacijami s homogenimi cikcak črtami in zaprtimi 2-celičnimi vložitvami usmerjenih Eulerjevih grafov v ploskve. Na koncu predstavimo aplikacijo na en tip ?$z$?-monodromije"}],"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-RWRF3E4I","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-RWRF3E4I"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-RWRF3E4I/d5662206-4670-4753-8094-11f20d85a892/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-RWRF3E4I/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-RWRF3E4I"}}}}