{"?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-IXAUSFAX/4a6e1b4e-03ba-4ef3-a7b8-60f2a210882f/PDF","dcterms:extent":"352 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-IXAUSFAX/4d6596c7-e904-4267-a51d-6750f7427866/TEXT","dcterms:extent":"29 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-IXAUSFAX","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2022","dc:creator":["Grunwald, Lilya A.","Mednykh, Ilya"],"dc:format":[{"@xml:lang":"sl","#text":"letnik:22"},{"@xml:lang":"sl","#text":"številka:4"},{"@xml:lang":"sl","#text":"str. 649-674"}],"dc:identifier":["DOI:10.26493/1855-3974.2029.01d","COBISSID_HOST:142189827","ISSN:1855-3966","URN:URN:NBN:SI:doc-IXAUSFAX"],"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":"Chebyshev polynomial"},{"@xml:lang":"en","#text":"circulant graph"},{"@xml:lang":"sl","#text":"krožni graf"},{"@xml:lang":"sl","#text":"Laplaceova matrika"},{"@xml:lang":"en","#text":"Laplacian matrix"},{"@xml:lang":"en","#text":"Mahler measure"},{"@xml:lang":"sl","#text":"Mahlerjeva mera"},{"@xml:lang":"sl","#text":"polinom Čebiševa"},{"@xml:lang":"en","#text":"rooted tree"},{"@xml:lang":"en","#text":"spanning forest"},{"@xml:lang":"sl","#text":"vkoreninjeno drevo"},{"@xml:lang":"sl","#text":"vpeti gozd"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"The number of rooted forests in circulant graphs|"},"dc:description":[{"@xml:lang":"sl","#text":"In this paper, we develop a new method to produce explicit formulas for the number ?$f_{G}(n)$? of rooted spanning forests in the circulant graphs ?$G=C_{n}(s_1,s_2,\\ldots,s_k)$? and ?$ G=C_{2n}(s_1,s_2,\\ldots,s_k,n)$?. These formulas are expressed through Chebyshev polynomials. We prove that in both cases the number of rooted spanning forests can be represented in the form ?$f_{G}(n)=p\\,a(n)^2$?, where ?$a(n)$? is an integer sequence and ?$p$? is a prescribed natural number depending on the parity of ?$n$?. Finally, we find an asymptotic formula for ?$f_{G}(n)$? through the Mahler measure of the associated Laurent polynomial ?$P(z) = 2k+1-\\sum\\limits_{i = 1}^k(z^{s_i}+z^{-s_i})$?"},{"@xml:lang":"sl","#text":"V članku razvijemo novo metodo izpeljave eksplicitnih formul za število ?$f_{G}(n)$? vkoreninjenih vpetih gozdov v krožnih grafih ?$G=C_{n}(s_1,s_2,\\ldots,s_k)$? in ?$G=C_{2n}(s_1,s_2,\\ldots,s_k,n)$?. Te formule so izražene s pomočjo polinomov Čebiševa. Dokažemo, da je v obeh primerih število vpetih vkoreninjenih gozdov mogoče predstaviti v obliki ?$f_{G}(n)=p\\,a(n)^2$?, kjer je ?$a(n)$? celoštevilsko zaporedje, ?$p$? pa naravno število, odvisno od parnosti števila ?$n$?. Poiščemo tudi asimptotsko formulo za ?$f_{G}(n)$? s pomočjo Mahlerjeve mere pridruženega Laurentovega polinoma ?$P(z)=2k+1-\\sum\\limits_{i=1}^k(z^{s_i}+z^{-s_i})$?"}],"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-IXAUSFAX","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-IXAUSFAX"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-IXAUSFAX/4a6e1b4e-03ba-4ef3-a7b8-60f2a210882f/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-IXAUSFAX/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-IXAUSFAX"}}}}