{"?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-U3P0O64V/dfe93372-8dfd-4926-b92e-37e0337bb0b5/PDF","dcterms:extent":"727 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-U3P0O64V/a64d5004-807a-433a-bdb4-6f5cbe6eaa85/TEXT","dcterms:extent":"28 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-U3P0O64V","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2019","dc:creator":["Győrffy, Lajos","Makay, Géza","Pluhár, András"],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:16"},{"@xml:lang":"sl","#text":"str. 97-109"}],"dc:identifier":["ISSN:1855-3966","COBISSID_HOST:18702937","URN:URN:NBN:SI:doc-U3P0O64V"],"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":"igra k-v-vrsti"},{"@xml:lang":"en","#text":"k-in-a-row game"},{"@xml:lang":"en","#text":"pairing strategies"},{"@xml:lang":"en","#text":"positional games"},{"@xml:lang":"sl","#text":"pozicijska igra"},{"@xml:lang":"sl","#text":"simetrije"},{"@xml:lang":"sl","#text":"strategije prirejanja"},{"@xml:lang":"en","#text":"symmetries"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"The pairing strategies of the 9-in-a-row game|"},"dc:description":[{"@xml:lang":"sl","#text":"One of the most useful strategies for proving Breaker's win in Maker-Breaker Positional Games is to find a pairing strategy. In some cases there are no pairing strategies at all, in some cases there are unique or almost unique strategies. For the ?$k$?-in-a-row game, the case ?$k = 9$? is the smallest (sharp) for which there exists a Breaker winning pairing (paving) strategy. One pairing strategy for this game was given by Hales and Jewett. In this paper we show that there are other winning pairings for the 9-in-a-row game, all have a very symmetric torus structure. While describing these symmetries we prove that there are only a finite number of non-isomorphic pairings for the game (around 200 thousand), which can be also listed up by a computer program. In addition, we prove that there are no \"irregular\", non-symmetric pairings. At the end of the paper we also show a pairing strategy for a variant of the 3-dimensional ?$k$?-in-a-row game"},{"@xml:lang":"sl","#text":"Ena od najbolj uporabnih strategij za dokaz zmage Drugega v pozicijskih igrah z dvema igralcema je najti strategijo prirejanja. V nekaterih primerih sploh ni strategije prirejanja, v nekaterih primerih je strategija ena sama ali pa jih je le peščica. Za igro ?$k$?-v-vrsti je primer ?$k = 9$? najmanjši (strogo), za katerega obstaja zmagovalna strategija prirejanja (tlakovanja). Eno strategijo prirejanja za to igro sta podala Hales in Jewett. V članku pokažemo, da obstajajo druga zmagovalna prirejanja za igro 9-v-vrsti, ki imajo vsa zelo simetrično strukturo svitka. Opisujoč te simetrije dokažemo, da obstaja samo končno število neizomorfnih prirejanj za to igro (okrog 200 tisoč), katerih seznam se da narediti z računalniškim programom. Poleg tega dokažemo, da ni nobenih \"iregularnih\", nesimetričnih prirejanj. Na koncu članka predstavimo tudi strategijo prirejanja za 3-dimenzionalno različico igre ?$k$?-v-vrsti"}],"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-U3P0O64V","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-U3P0O64V"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-U3P0O64V/dfe93372-8dfd-4926-b92e-37e0337bb0b5/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-U3P0O64V/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-U3P0O64V"}}}}