{"?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-RJL5NGNH/1e230c10-1a5b-4ece-b86a-c42926c30d40/PDF","dcterms:extent":"377 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-RJL5NGNH/ab38749b-93b6-45c9-a11e-150c8663ddfb/TEXT","dcterms:extent":"45 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-RJL5NGNH","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2019","dc:creator":["García-García, Juan Ignacio","Marín-Aragón, Daniel","Moreno-Frías, María Ángeles","Rosales, José Carlos","Vigneron-Tenorio, Alberto"],"dc:format":[{"@xml:lang":"sl","#text":"letnik:17"},{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"str. 397-417"}],"dc:identifier":["ISSN:1855-3966","COBISSID_HOST:18957145","URN:URN:NBN:SI:doc-RJL5NGNH"],"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":"embedding dimension"},{"@xml:lang":"en","#text":"Frobenius number"},{"@xml:lang":"sl","#text":"Frobeniusovo število"},{"@xml:lang":"en","#text":"genus"},{"@xml:lang":"en","#text":"multiplicity"},{"@xml:lang":"en","#text":"numerical semigroup"},{"@xml:lang":"sl","#text":"rod"},{"@xml:lang":"sl","#text":"večkratnost"},{"@xml:lang":"sl","#text":"vložitvena dimenzija"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Semigroups with fixed multiplicity and embedding dimension|"},"dc:description":[{"@xml:lang":"sl","#text":"Given ?$m \\in \\mathbb{N}$?, a numerical semigroup with multiplicity ?$m$? is called a packed numerical semigroup if its minimal generating set is included in ?$\\{m, m + 1, \\dots, 2m - 1 \\}$?. In this work, packed numerical semigroups are used to build the set of numerical semigroups with a given multiplicity and embedding dimension, and to create a partition of this set. Wilf's conjecture is verified in the tree associated to some packed numerical semigroups. Furthermore, given two positive integers ?$m$? and ?$e$?, some algorithms for computing the minimal Frobenius number and minimal genus of the set of numerical semigroups with multiplicity ?$m$? and embedding dimension ?$e$? are provided. We also compute the semigroups where these minimal values are achieved"},{"@xml:lang":"sl","#text":"Pri danem ?$m \\in \\mathbb{N}$? se številska polgrupa z večkratnostjo ?$m$? imenuje pakirana številska polgrupa, če je njena minimalna množica generatorjev vsebovana v ?$\\{m, m + 1, \\dots, 2m - 1 \\}$?. V članku so pakirane številske polgrupe uporabljene za izgradnjo množice številskih polgrup z dano večkratnostjo in vložitveno dimenzijo ter za tvorbo razčlenitve te množice. Wilfova domneva je potrjena v drevesu, pridruženem nekaterim pakiranim številskim polgrupam. Nadalje, če sta dani dve pozitivni celi števili ?$m$? in ?$e$?, je podanih nekaj algoritmov za izračun minimalnega Frobeniusovega števila in minimalnega rodu množice številskih polgrup z večkratnostjo ?$m$? in vložitveno dimenzijo ?$e$?. Izračunamo tudi polgrupe, pri katerih so te minimalne vrednosti dosežene"}],"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-RJL5NGNH","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-RJL5NGNH"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-RJL5NGNH/1e230c10-1a5b-4ece-b86a-c42926c30d40/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-RJL5NGNH/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-RJL5NGNH"}}}}