{"?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-1JB7GEWT/C053B333-49B6-4048-934D-103DBD5EF80D/PDF","dcterms:extent":"0 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-1JB7GEWT/eac7612c-5357-41fb-9bb4-fab4b1b118ed/PDF","dcterms:extent":"333 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-1JB7GEWT/7a49fe83-b513-492b-84fd-9c6a4add9682/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-1JB7GEWT","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2011","dc:creator":["Shuchat, Alan","Shull, Randy","Trenk, Ann N."],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:4"},{"@xml:lang":"sl","#text":"str. 95-109"}],"dc:identifier":["COBISSID:16263513","ISSN:1855-3966","URN:URN:NBN:SI:doc-1JB7GEWT"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Društvo matematikov, fizikov in astronomov Slovenije"},"dc:subject":[{"@xml:lang":"sl","#text":"delno urejene množice"},{"@xml:lang":"en","#text":"fractional weak discrepancy"},{"@xml:lang":"sl","#text":"popolnoma linearna neskladnost"},{"@xml:lang":"en","#text":"posets"},{"@xml:lang":"sl","#text":"šibka neskladnost"},{"@xml:lang":"en","#text":"total linear discrepancy"},{"@xml:lang":"en","#text":"weak discrepancy"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"The total weak discrepancy of a partially ordered set|"},"dc:description":{"@xml:lang":"sl","#text":"We define the total weak discrepancy of a poset ?$P$? as the minimum nonnegative integer ?$k$? for which there exists a function ?$f : V \\to {\\mathbf Z}$? satisfying (i) if ?$a \\prec b$? then ?$f(a) + 1 \\leq f(b)$? and (ii) ?$\\sum|f(a) - f(b)| \\leq k$?, where the sum is taken over all unordered pairs ?$\\{a, b\\}$? of incomparable elements. If we allow ?$k$? and ?$f$? to take real values, we call the minimum ?$k$? the fractional total weak discrepancy of ?$P$?. These concepts are related to the notions of weak and fractional weak discrepancy, where (ii) must hold not for the sum but for each individual pair of incomparable elements of $P$. We prove that, unlike the latter, the total weak and fractional total weak discrepancy of ?$P$? are always the same, and we give a polynomial-time algorithm to find their common value. We use linear programming duality and complementary slackness to obtain this result"},"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-1JB7GEWT","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-1JB7GEWT"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-1JB7GEWT/C053B333-49B6-4048-934D-103DBD5EF80D/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-1JB7GEWT/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-1JB7GEWT"}}}}