{"?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-AM4SY3Z3/6192284b-bc1d-40f6-ba42-4df26cab82b6/PDF","dcterms:extent":"365 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-AM4SY3Z3/285a2dc7-b916-4456-9e28-fa7d8cb645ea/TEXT","dcterms:extent":"24 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-AM4SY3Z3","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2014","dc:creator":["Konstantinova, Elena","Medvedev, Alexey"],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:7"},{"@xml:lang":"sl","#text":"str. 237-246"}],"dc:identifier":["COBISSID:16797273","ISSN:1855-3966","URN:URN:NBN:SI:doc-AM4SY3Z3"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Društvo matematikov, fizikov in astronomov Slovenije"},"dc:subject":[{"@xml:lang":"en","#text":"Cayley graphs"},{"@xml:lang":"en","#text":"cycle embedding"},{"@xml:lang":"sl","#text":"grafi"},{"@xml:lang":"en","#text":"Pancake graph"},{"@xml:lang":"en","#text":"small cycles"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Small cycles in the Pancake graph|"},"dc:description":{"@xml:lang":"sl","#text":"The Pancake graph is well known because of the open Pancake problem. It has the structure that any ?$l$?-cycle, ?$6 \\leqslant l \\leqslant n!$?, can be embedded in the Pancake graph ?$P_n$?, ?$n \\geqslant 3$?. Recently it was shown that there are exactly ?$\\frac{n!}{6}$? independent 6-cycles and ?$n!(n - 3)$? distinct 7-cycles in the graph. In this paper we characterize all distinct 8-cycles by giving their canonical forms as products of generating elements. It is shown that there are exactly ?$\\frac{n!(n^3 + 12n^2 - 103n + 176)}{16}$? distinct 8-cycles in ?$P_n$?, ?$n \\geqslant 4$?. A maximal set of independent 8-cycles contains? $\\frac{n!}{8}$? of these"},"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-AM4SY3Z3","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-AM4SY3Z3"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-AM4SY3Z3/6192284b-bc1d-40f6-ba42-4df26cab82b6/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-AM4SY3Z3/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-AM4SY3Z3"}}}}