{"?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-SUIXV9AY/fa093197-cc48-4538-99c6-50e5f55e66c9/PDF","dcterms:extent":"292 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-SUIXV9AY/961417dd-68e5-453c-8257-2fbe689d2ad2/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-SUIXV9AY","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2016","dc:creator":"Stokes, Klara","dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:10"},{"@xml:lang":"sl","#text":"str. 169-181"}],"dc:identifier":["COBISSID:17735257","ISSN:1855-3966","URN:URN:NBN:SI:doc-SUIXV9AY"],"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":"configuration"},{"@xml:lang":"en","#text":"construction"},{"@xml:lang":"en","#text":"enumeration"},{"@xml:lang":"sl","#text":"ireducibilen"},{"@xml:lang":"en","#text":"irreducible"},{"@xml:lang":"sl","#text":"konfiguracija"},{"@xml:lang":"sl","#text":"konstrukcija"},{"@xml:lang":"sl","#text":"parcialni linearni prostor"},{"@xml:lang":"en","#text":"partial linear space"},{"@xml:lang":"sl","#text":"preštevanje"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Irreducibility of configurations|"},"dc:description":[{"@xml:lang":"sl","#text":"In Annali di Mat. (2) 15, 1--26 (1887), V. Martinetti enumerated small ?$v_3$?-configurations. One of his tools was a construction that permits to produce a ?$(v+1)_3$?-configuration from a ?$v_3$?-configuration. He called configurations that were not constructible in this way irreducible configurations. According to his definition, the irreducible configurations are Pappus' configuration and four infinite families of configurations. In 2005, M. Boben Reductions of ?$(v_3)$? configurations, Preprint, \\url{arXiv:math/0505136v1} defined a simpler and more general definition of irreducibility, for which only two ?$v_3$?-configurations, the Fano plane and Pappus' configuration, remained irreducible. The present article gives a generalization of Boben's reduction for both balanced and unbalanced? $(v_r,b_k)$?-configurations, and proves several general results on augmentability and reducibility. Motivation for this work is found, for example, in the counting and enumeration of configurations"},{"@xml:lang":"sl","#text":"V članku iz leta 1886 je Martinetti preštel majhne ?$v_3$?-konfiguracije. Eno od njegovih orodij je bilo konstrukcija, ki omogoča dobiti ?$(v+1)_3$?-konfiguracijo iz ?$v_3$?-konfiguracije. Konstrukcije, ki jih ni mogoče konstruirati na ta način, je imenoval ireducibilne konfiguracije. V skladu z njegovo definicijo so ireducibilne konfiguracije Pappusova konfiguracija ter štiri neskončne družine konfiguracij. Leta 2005 je Boben iznašel preprostejšo in splošnejšo definicijo ireducibilnosti, po kateri sta ostali nereducibilni samo dve ?$v_3$?-konfiguraciji, in sicer Fanova ravnina in Pappusova konfiguracija. Ta članek posplošuje Bobenovo redukcijo tako na uravnotežene kot neuravnotežene ?$(v_r,b_k)$?-konfiguracije, in dokaže več splošnih rezultatov v zvezi z augmentabilnostjo in reducibilnostjo. Motivacija za to delo je, na primer, štetje in preštevanje konfiguracij"}],"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-SUIXV9AY","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-SUIXV9AY"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-SUIXV9AY/fa093197-cc48-4538-99c6-50e5f55e66c9/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-SUIXV9AY/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-SUIXV9AY"}}}}