{"?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-7P1EQ4WA/ff74baf0-e736-4e70-8e67-dcca4dad3158/PDF","dcterms:extent":"525 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-7P1EQ4WA/19dbdb54-7cdc-43a8-bd19-2b821d0ad2a7/TEXT","dcterms:extent":"36 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-7P1EQ4WA","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":["Berman, Leah","Mitchell, William H."],"dc:format":[{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"letnik:9"},{"@xml:lang":"sl","#text":"str. 165-186"}],"dc:identifier":["COBISSID:17588569","ISSN:1855-3966","URN:URN:NBN:SI:doc-7P1EQ4WA"],"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":"configurations"},{"@xml:lang":"sl","#text":"konfiguracije"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Sparse line deletion constructions for symmetric 4-configurations|"},"dc:description":[{"@xml:lang":"sl","#text":"A 4-configuration is a collection of points and lines in the Euclidean plane such that each point lies on four lines and each line passes through four points. In this paper we introduce a new family of these objects. Our construction generalizes a 2010 result of Berman and Grünbaum in which suitable 4-configurations from the well-understood celestial family are altered to yield new configurations with reduced geometric symmetry groups. The construction introduced in 2010 removes every other line of a symmetry class from the celestial configuration; here we give conditions under which every ?$p$?-th line can be removed, for ?$p \\in \\{2, 3, 4, \\cdots \\}$?. The geometric symmetry groups of the new configurations we obtain are of correspondingly smaller index as subgroups of the symmetry group of the underlying celestial configuration. These sparse constructions can also be repeated and combined to yield a rich variety of previously unknown 4-configurations. In particular, we can begin with a configuration with very high geometric symmetry - the dihedral symmetry of an ?$m$?-gon for ?$m$? quite large - and produce a configuration whose only geometric symmetry is ?$180^\\circ$ rotation?"},{"@xml:lang":"sl","#text":"4-konfiguracija je zbirka točk in premic v evklidski ravnini, pri kateri vsaka točka leži na štirih premicah, vsaka premica pa gre skozi štiri točke. V tem članku vpeljemo novo družino teh objektov. Naša konstrukcija posplošuje rezultat Bermanove in Grünbauma iz 2010, kjer so primerne 4-konfiguracije iz dobro razumljene družine zvezdnih konfiguracij spremenjene tako, da iz njih nastanejo nove konfiguracije z manjšimi grupami geometrijskih simetrij. Konstrukcija iz 2010 odstrani vsako drugo premico iz simetrijskega razreda iz zvezdne konfiguracije; tukaj podamo pogoje, pod katerimi lahko odstranimo vsako ?$p$?-to premico, za ?$p \\in \\{2, 3, 4, \\cdots \\}$?. Grupe geometrijskih simetrij novih konfiguracij, ki jih dobimo na ta način, so ustrezno manjšega indeksa kot podgrupe simetrijske grupe prvotne zvezdne konfiguracije. Te redke konstrukcije lahko tudi ponavljamo in kombiniramo ter na ta način dobimo bogato zbirko prej neznanih 4-konfiguracij. Tako lahko npr. začnemo s konfiguracijo z zelo bogato geometrijsko simetrijo - diedrsko simetrijo ?$m$?-kotnika za precej velik ?$m$? - in iz nje dobimo konfiguracijo, katere edina geometrijska simetrija je rotacija za ?$180^\\circ$?"}],"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-7P1EQ4WA","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-7P1EQ4WA"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-7P1EQ4WA/ff74baf0-e736-4e70-8e67-dcca4dad3158/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-7P1EQ4WA/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-7P1EQ4WA"}}}}