{"?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-4179UIA5/bfbb42a0-f517-48be-af77-cadf9b7491ac/PDF","dcterms:extent":"280 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-4179UIA5/a58c5b59-331e-4fe8-b4d2-c268ba164395/TEXT","dcterms:extent":"21 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-4179UIA5/0bccf1c7-e8ab-4a26-a5ab-8f3e290cb44a/PDF","dcterms:extent":"166 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-4179UIA5/7f4ed8d8-e93a-417d-a32d-2a75a4735517/TEXT","dcterms:extent":"3 KB"}],"edm:TimeSpan":{"@rdf:about":"2008-2026","edm:begin":{"@xml:lang":"en","#text":"2008"},"edm:end":{"@xml:lang":"en","#text":"2026"}},"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:doc-4179UIA5","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2026","dc:creator":"Patkós, Balázs","dc:format":[{"@xml:lang":"sl","#text":"številka:2, article  p2.07"},{"@xml:lang":"sl","#text":"letnik:26"},{"@xml:lang":"sl","#text":"str. 1-7"}],"dc:identifier":["DOI:10.26493/1855-3974.3528.e84","ISSN:1855-3974","COBISSID_HOST:289325315","URN:URN:NBN:SI:doc-4179UIA5"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem"},"dc:subject":[{"@xml:lang":"en","#text":"diversity"},{"@xml:lang":"en","#text":"intersecting families"},{"@xml:lang":"sl","#text":"minimalna stopnja"},{"@xml:lang":"en","#text":"minimum degree"},{"@xml:lang":"sl","#text":"presečne družine"},{"@xml:lang":"sl","#text":"raznolikost"}],"dcterms:temporal":{"@rdf:resource":"2008-2026"},"dc:title":{"@xml:lang":"sl","#text":"Size, diversity, minimum degree, sturdiness, dömdödöm|"},"dc:description":[{"@xml:lang":"sl","#text":"For a family F of sets and a disjoint pair A, B we let F(A, overline(B)) = F ? F: A ? F, B ? F = Ř}.The (p,q)-dömdödöm of a family F ? 2n is ß(p, q)(F)=min {|F(A, overline(B))|:|A|=p,|B|=q, A ? B = Ř, A, B ? n}. This definition encompasses size, diversity, minimum degree, and sturdiness as special cases. We investigate the maximum possible value ß(p, q)(n,k) of ß(p, q)(F) over all k-uniform intersecting families F ? 2n. We determine the order of magnitude of ß(p, q)(n,k) for all fixed p,q,k. We relate the asymptotics of ß(p, q)(n,k) to the constant value of ß(0, q)(n,q+1) and establish ß(p, 1)(n,k)=\\binom{n-3-p}{k-2-p} and ß(p, 2)(n,k)= 2\\binom{n-5}{k-3-p} -\\binom{n-7}{k-5-p} if n is large enough"},{"@xml:lang":"sl","#text":"Za družino množic F in nepovezan par A,B definiramo F(A, overline(B)) = F ? F: A ? F, B ? F = Ř}. (p, q)-dömdödöm družine F ? 2n je ß(p, q)(F)=min {|F(A, overline(B))|:|A|=p,|B|=q, A ? B = Ř, A, B ? n}. Ta definicija zajema velikost, raznolikost, minimalno stopnjo in trdnost kot posebne primere. Preučujemo največjo možno vrednost ß(p, q)(n,k), tj. vrednost ß(p, q)(F) med vsemi k-uniformnimi presečnimi družinami F ? 2n. Določimo red velikosti ß(p, q)(n,k) za vse fiksne vrednosti p, q, k. Asimptotiko ß(p, q)(n,k) povežemo s konstanto ß(0, q)(n,q+1) ter dokažemo, da za dovolj velik n velja ß(p, 1)(n,k)=\\binom{n-3-p}{k-2-p} in ß(p, 2)(n,k)= 2\\binom{n-5}{k-3-p} -\\binom{n-7}{k-5-p}"}],"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-4179UIA5","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-4179UIA5"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-4179UIA5/bfbb42a0-f517-48be-af77-cadf9b7491ac/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-4179UIA5/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-4179UIA5"}}}}