{"?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-CFMDOQQY/6b0375ce-76ff-4633-815c-652d630c2639/PDF","dcterms:extent":"351 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-CFMDOQQY/081bf7da-9403-4bf5-9a3b-c55dce0ac417/TEXT","dcterms:extent":"46 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-CFMDOQQY","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":"Tuffley, Christopher","dc:format":[{"@xml:lang":"sl","#text":"letnik:16"},{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"str. 331-348"}],"dc:identifier":["ISSN:1855-3966","COBISSID_HOST:18755161","URN:URN:NBN:SI:doc-CFMDOQQY"],"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":"complete n-complex"},{"@xml:lang":"en","#text":"intrinsic linking"},{"@xml:lang":"sl","#text":"intrinzično povezovanje"},{"@xml:lang":"sl","#text":"polni n-kompleks"},{"@xml:lang":"en","#text":"Ramsey theory"},{"@xml:lang":"sl","#text":"Ramseyeva teorija"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Intrinsic linking with linking numbers of specified divisibility|"},"dc:description":[{"@xml:lang":"sl","#text":"Let ?$n$?, ?$q$? and ?$r$? be positive integers, and let ?$K_N^n$? be the ?$n$?-skeleton of an ?$(N - 1)$?-simplex. We show that for ?$N$? sufficiently large every embedding of ?$K_N^n$? in ?$\\mathbb{R}^{2n + 1}$? contains a link consisting of ?$r$? disjoint ?$n$?-spheres, such that every pairwise linking number is a nonzero multiple of ?$q$?. This result is new in the classical case ?$n = 1$? (graphs embedded in ?$\\mathbb{R}^3$?) as well as the higher dimensional cases ?$n \\geq 2$?; and since it implies the existence of an ?$r$?-component link with all pairwise linking numbers at least ?$q$? in absolute value, it also extends a result of Flapan et al. from ?$n = 1$? to higher dimensions. Additionally, for ?$r = 2$? we obtain an improved upper bound on the number of vertices required to force a two-component link with linking number a nonzero multiple of ?$q$?. Our new bound has growth ?$O(nq^2)$?, in contrast to the previous bound of growth ?$O(\\sqrt{n}4^nq^{n + 2})$?"},{"@xml:lang":"sl","#text":"Naj bodo ?$n$?, ?$q$? in ?$r$? pozitivna cela števila, ?$K_N^n$? pa naj bo ?$n$?-skelet ?$(N - 1)$?-simpleksa. Pokažemo, da za dovolj velik ?$N$? vsaka vložitev ?$K_N^n$? v ?$\\mathbb{R}^{2n + 1}$? vsebuje splet, ki sestoji iz ?$r$? disjunktnih ?$n$?-sfer, tako da je vsako po parih spletno število neničelni večkratnik števila ?$q$?. Ta rezultat je nov v klasičnem primeru ?$n = 1$? (grafi vloženi v ?$\\mathbb{R}^3$?) kot tudi v višjedimenzionalnih primerih ?$n \\geq 2$?; in ker implicira obstoj ?$r$?-komponentnega spleta z vsemi po parih spletnimi števili, katerih absolutna vrednost je najmanj ?$q$?, razširja tudi rezultat, ki so ga dobili Flapan idr. za ?$n = 1$? na višje dimenzije. Poleg tega, za ?$r = 2$? dobimo izboljšano zgornjo mejo za število točk, potrebnih za izsiljenje dvo-komponentnega spleta s spletnim številom, ki je neničelni večkratnik števila ?$q$?. Naša nova meja ima rast ?$O(nq^2)$?, v nasprotju s prejšnjo mejo rasti ?$O(\\sqrt{n}4^nq^{n + 2})$?"}],"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-CFMDOQQY","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-CFMDOQQY"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-CFMDOQQY/6b0375ce-76ff-4633-815c-652d630c2639/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-CFMDOQQY/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-CFMDOQQY"}}}}