{"?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-QFLURZ74/b495d095-dcda-4549-9eb9-00e8e22257a2/PDF","dcterms:extent":"342 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-QFLURZ74/d42e9d59-385d-4d5f-9b49-4aca35596bf1/TEXT","dcterms:extent":"49 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-QFLURZ74","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2015","dc:creator":"Kainen, Paul C.","dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:9"},{"@xml:lang":"sl","#text":"str. 27-43"}],"dc:identifier":["COBISSID:17577817","ISSN:1855-3966","URN:URN:NBN:SI:doc-QFLURZ74"],"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":"Cayley graph"},{"@xml:lang":"sl","#text":"Cayleyjev graf"},{"@xml:lang":"sl","#text":"dobro-urejeno zaporedje"},{"@xml:lang":"en","#text":"forcing commutativity"},{"@xml:lang":"en","#text":"geodesic cycle"},{"@xml:lang":"sl","#text":"geodetski cikel"},{"@xml:lang":"en","#text":"groupoid diagram"},{"@xml:lang":"sl","#text":"grupoidni diagram"},{"@xml:lang":"sl","#text":"hiperkocka"},{"@xml:lang":"en","#text":"hypercube"},{"@xml:lang":"en","#text":"robust cycle basis"},{"@xml:lang":"sl","#text":"robustna baza ciklov"},{"@xml:lang":"sl","#text":"vsiljena komutativnost"},{"@xml:lang":"en","#text":"well-arranged sequence"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Cycle construction and geodesic cycles with application to the hypercube|"},"dc:description":[{"@xml:lang":"sl","#text":"Construction of cycles in a graph is investigated, where cycles from particular subsets (such as bases) are added together so that each partial sum is also a cycle or each new cycle intersects the sum of the preceding terms in a nontrivial path. Starting with the geodesic cycles, a hierarchical construction is given. For the hypercube graph, geodesic cycles are characterized, and it is shown how hypercube geodesic cycles can be constructed in two steps from a special basis. Applications are given to inferring commutativity of a diagram in a groupoid from commutativity of some of its cycles"},{"@xml:lang":"sl","#text":"Raziskujemo konstrukcijo ciklov v grafu, pri čemer se cikli iz posebnih podmnožic (kot so npr. baze) seštevajo tako, da je vsaka delna vsota tudi cikel ali pa vsak nov cikel seka vsoto prejšnjih členov v netrivialni poti. Izhajajoč iz geodetskih ciklov postavimo hierarhično konstrukcijo. Za graf hiperkocke karakteriziramo geodetske cikle in pokažemo, kako jih lahko konstruiramo v dveh korakih iz posebne baze. Ena od uporab: komutativnost diagrama v grupoidu sledi iz komutativnosti nekaterih od njegovih ciklov"}],"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-QFLURZ74","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-QFLURZ74"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-QFLURZ74/b495d095-dcda-4549-9eb9-00e8e22257a2/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-QFLURZ74/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-QFLURZ74"}}}}