{"?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-MFG02KK6/d99406d1-bfa3-41c4-844d-be361395f53e/PDF","dcterms:extent":"364 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-MFG02KK6/521c3d31-d7b3-472e-a072-d8800143ae7b/TEXT","dcterms:extent":"20 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-MFG02KK6","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2015","dc:creator":["Blecher, Aubrey","Brennan, Charlotte","Knopfmacher, Arnold"],"dc:format":[{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"letnik:9"},{"@xml:lang":"sl","#text":"str. 287-300"}],"dc:identifier":["COBISSID:17609305","ISSN:1855-3966","URN:URN:NBN:SI:doc-MFG02KK6"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije"},"dc:subject":[{"@xml:lang":"sl","#text":"asimptotično vedenje"},{"@xml:lang":"en","#text":"asymptotics"},{"@xml:lang":"en","#text":"bargraphs"},{"@xml:lang":"en","#text":"generating functions"},{"@xml:lang":"en","#text":"levels"},{"@xml:lang":"sl","#text":"rodovne funkcije"},{"@xml:lang":"sl","#text":"stopničasti grafi"},{"@xml:lang":"sl","#text":"terase"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Levels in bargraphs|"},"dc:description":[{"@xml:lang":"sl","#text":"Bargraphs are lattice paths in ?$\\mathbb{N}_0^2$?, which start at the origin and terminate immediately upon return to the ?$x$?-axis. The allowed steps are the up step ?$(0,1)$?, the down step ?$(0,-1)$? and the horizontal step ?$(1,0)$?. The first step is an up step and the horizontal steps must all lie above the ?$x$?-axis. An up step cannot follow a down step and vice versa. In this paper we consider levels, which are maximal sequences of two or more adjacent horizontal steps. We find the generating functions that count the total number of levels, the leftmost ?$x$?-coordinate and the height of the first level and obtain the generating function for the mean of these parameters. Finally, we obtain the asymptotics of these means as the length of the path tends to infinity"},{"@xml:lang":"sl","#text":"Stopničasti grafi so mrežne poti v ?$\\mathbb{N}_0^2$?, ki se začnejo v koordinatnem izhodišču, končajo pa takoj ko se vrnejo na abscisno os. Dovoljeni koraki so korak navzgor ?$(0,1)$?, korak navzdol ?$(0,-1)$? in vodoravni korak ?$(1,0)$?. Prvi korak je vselej korak navzgor, vodoravni koraki pa morajo vsi ležati nad abscisno osjo. Koraku navzgor ne more slediti korak navzdol, in obratno. V tem članku obravnavamo t.i. terase, maksimalna zaporedja dveh ali več sosednjih vodoravnih korakov. Poiščemo rodovne funkcije, ki preštevajo skupno število nivojev, skrajno levo absciso in višino prve terase in izpeljemo rodovno funkcijo za povprečno vrednost teh parametrov. Nazadnje opišemo asimptotično vedenje teh sredin, ko gre dolžina poti v neskončnost"}],"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-MFG02KK6","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-MFG02KK6"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-MFG02KK6/d99406d1-bfa3-41c4-844d-be361395f53e/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-MFG02KK6/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-MFG02KK6"}}}}