{"?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-7B0N0IIU/946e5957-0c5e-4fa0-aa39-7ad6f81b8232/PDF","dcterms:extent":"2370 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-7B0N0IIU/ddf22c71-9b6c-4df8-874b-a722b33640aa/TEXT","dcterms:extent":"37 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-7B0N0IIU","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":["Gross, Jonathan L.","Khan, Imran F.","Poshni, Mehvish Irfan"],"dc:format":[{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"letnik:7"},{"@xml:lang":"sl","#text":"str. 423-440"}],"dc:identifier":["COBISSID:17065305","ISSN:1855-3966","URN:URN:NBN:SI:doc-7B0N0IIU"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Društvo matematikov, fizikov in astronomov Slovenije"},"dc:subject":[{"@xml:lang":"en","#text":"3-prism"},{"@xml:lang":"en","#text":"3-wheel"},{"@xml:lang":"en","#text":"genus distribution"},{"@xml:lang":"en","#text":"partitioned genus distribution"},{"@xml:lang":"en","#text":"production"},{"@xml:lang":"en","#text":"rooted-graph"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Genus distributions of iterated 3-wheels and 3-prisms|"},"dc:description":{"@xml:lang":"sl","#text":"The iterated 3-prism ?$Pr_3^n$? is the cartesian product ?$C_3 \\Box P_n$? of a 3-cycle and an ?$n$?-vertex path. At each end of the iterated 3-prism, there is a 3-cycle whose vertices are 3-valent in ?$C_3 \\Box P_n$?. The iterated 3-wheel ?$W_3^n$? is obtained by contracting one of these 3-cycles in ?$C_3 \\Box P_{n+1}$? to a single vertex. Using rooted-graphs, we derive simultaneous recursions for the partitioned genus distributions of ?$W_3^n$? and a formula for the genus distribution of the graphs ?$Pr_3^n$?. A seemingly straightforward way to construct either the sequence of iterated prisms ?$Pr_3^n$? or the sequence of iterated wheels ?$W_3^n$?, would be by iterative amalgamation of a copy of ?$C_3 \\Box K_2$?, such that a copy of ?$C_3$? contained in it is matched to the \"newest\" copy of ?$C_3$? in the growing graph. Calculating genus distributions for the sequences would then involve an excessively large set of simultaneous recurrences. To avoid this, we propose a method of iterative surgery, under which the same vertex is considered a root-vertex in all graphs of the sequence, and in which the successive calculations of genus distributions require only four simultaneous recurrences. We also prove that the genus distribution of ?$Pr_3^n$? not only dominates the genus distribution of ?$W_3^{n-1}$?, but is also dominated by the genus distribution of ?$W_3^n$?"},"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-7B0N0IIU","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-7B0N0IIU"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-7B0N0IIU/946e5957-0c5e-4fa0-aa39-7ad6f81b8232/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-7B0N0IIU/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-7B0N0IIU"}}}}