{"?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-DKC631PC/82a05e99-59a3-4f0d-9128-e0832dd4ca57/PDF","dcterms:extent":"326 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-DKC631PC/639489d8-3925-4126-8248-0860de2eed75/TEXT","dcterms:extent":"36 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-DKC631PC/eaf885b7-95e2-487b-abd9-9501bf535086/PDF","dcterms:extent":"170 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-DKC631PC/3ea7264c-eb66-4ce1-989d-6b8e845d0ea5/TEXT","dcterms:extent":"4 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-DKC631PC/c2bb388d-4a74-4c36-b863-f5446050c8c1/PDF","dcterms:extent":"170 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-DKC631PC/a825f043-bfea-48e5-9792-bf9cc476052c/TEXT","dcterms:extent":"4 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-DKC631PC","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2023","dc:creator":["O'Reilly-Regueiro, Eugenia O'Reilly-Regueiro","Rodríguez-Fitta, José Emanuel"],"dc:format":[{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"letnik:23"},{"@xml:lang":"sl","#text":"P2.04 (14 str.)"}],"dc:identifier":["DOI:10.26493/1855-3974.2415.fd1","COBISSID_HOST:150274307","ISSN:1855-3966","URN:URN:NBN:SI:doc-DKC631PC"],"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":"automorphism groups of designs"},{"@xml:lang":"en","#text":"flag-transitivity"},{"@xml:lang":"sl","#text":"grupa avtomorfizmov dizajnov"},{"@xml:lang":"sl","#text":"praporna tranzitivnost"},{"@xml:lang":"en","#text":"primitive groups"},{"@xml:lang":"sl","#text":"primitivne grupe"},{"@xml:lang":"sl","#text":"simetrični dizajni"},{"@xml:lang":"en","#text":"symmetric-designs"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"A parametrisation for symmetric designs admitting a flag-transitive, point-primitive automorphism group with a product action|"},"dc:description":[{"@xml:lang":"sl","#text":"We study ?$(v, \\, k,\\, \\lambda)$?-symmetric designs having a flag-transitive, point-primitive automorphism group, with ?$v=m^2$? and ?$(k, \\, \\lambda)=t>1$?, and prove that if ?$D$? is such a design with ?$m$? even admitting a flag-transitive, point-primitive automorphism group ?$G$?, then either: (1) ?$D$? is a design with parameters ?$\\left((2t+s-1)^2, \\frac{2t^2-(2-s)t)}{s}, \\frac{t^2-t)}{s^2}\\right)$? with ?$s\\ge 1$? odd, or (2) ?$G$? does not have a non-trivial product action. We observe that the parameters in (1), when ?$s=1$?, correspond to Menon designs. We also prove that if ?$D$? is a ?$(v, \\, k,\\, \\lambda)$?-symmetric design with a flag-transitive, point-primitive automorphism group of product action type with ?$v=m^l$? and ?$l\\ge 2$? then the complement of ?$D$? does not admit a flag-transitive automorphism group"},{"@xml:lang":"sl","#text":"Preučujemo ?$(v, \\, k,\\, \\lambda)$?-simetrične dizajne, ki imajo praporno tranzitivno in točkovno primitivno grupo avtomorfizmov, kjer je ?$v=m^2$? in ?$(k, \\, \\lambda)=t>1$?, ter dokažemo, da če je ?$D$? dizajn s sodim ?$m$?, ki dopušča praporno tranzitivno in točkovno primitivno grupo avtomorfizmov ?$G$?, potem velja bodisi: (1) ?$D$? je dizajn s parametri ?$\\left((2t+s-1)^2, \\frac{2t^2-(2-s)t)}{s}, \\frac{t^2-t)}{s^2}\\right)$?, kjer je ?$s\\ge 1$? lih, bodisi (2) ?$G$? nima netrivialnega produktnega delovanja. Opazimo, da parametri v (1), kadar je ?$s=1$?, ustrezajo Menonovim dizajnom. Dokažemo tudi, da če je ?$D$ $(v, \\, k,\\, \\lambda)$?-simetričen dizajn s praporno tranzitivno in točkovno primitivno grupo avtomorfizmov s produktnim delovanjem, kjer je ?$v=m^l$? in ?$l\\ge 2$?, potem komplement dizajna ?$D$? ne dopušča praporno tranzitivne grupe avtomorfizov"}],"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-DKC631PC","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-DKC631PC"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-DKC631PC/82a05e99-59a3-4f0d-9128-e0832dd4ca57/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-DKC631PC/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-DKC631PC"}}}}