{"?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-UVH09HRJ/8db13e6e-7e0f-47aa-8cf3-8c5cfa84e756/PDF","dcterms:extent":"422 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-UVH09HRJ/61779128-bdb3-4220-b580-9777550ac488/TEXT","dcterms:extent":"51 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-UVH09HRJ","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2021","dc:creator":["Elizalde, Sergi","Flórez, Rigoberto Flórez","Ramírez, José Luis"],"dc:format":[{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"letnik:21"},{"@xml:lang":"sl","#text":"str. 219-241"}],"dc:identifier":["DOI:10.26493/1855-3974.2478.d1b","COBISSID_HOST:112534019","ISSN:1855-3966","URN:URN:NBN:SI:doc-UVH09HRJ"],"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":"Fibonacci number"},{"@xml:lang":"sl","#text":"Fibonaccijevo število"},{"@xml:lang":"en","#text":"generating function"},{"@xml:lang":"sl","#text":"nepadajoča Dyckova pot"},{"@xml:lang":"en","#text":"non-decreasing Dyck path"},{"@xml:lang":"en","#text":"Riordan array"},{"@xml:lang":"sl","#text":"Riordanova matrika"},{"@xml:lang":"sl","#text":"rodovna funkcija"},{"@xml:lang":"sl","#text":"simetričen vrh"},{"@xml:lang":"en","#text":"symmetric peak"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Enumerating symmetric peaks in non-decreasing Dyck paths|"},"dc:description":[{"@xml:lang":"sl","#text":"Local maxima and minima of a Dyck path are called peaks and valleys, respectively. A Dyck path is non-decreasing if the heights (?$y$?-coordinates) of its valleys increase from left to right. A peak is symmetric if it is surrounded by two valleys (or endpoints of the path) at the same height. In this paper we give multivariate generating functions, recurrence relations, and closed formulas to count the number of symmetric and asymmetric peaks in non-decreasing Dyck paths. Finally, we use Riordan arrays to study weakly symmetric peaks, namely those for which the valley preceding the peak is at least as high as the valley following it"},{"@xml:lang":"sl","#text":"Lokalni maksimumi in minimumi Dyckovih poti se imenujejo vrhovi in doline. Dyckova pot je nepadajoča, če višine (?$y$?-koordinate) njenih dolin naraščajo od leve proti desni. Vrh je simetričen, če je obdan z dvema dolinama (oz. krajiščema poti) na isti višini. V tem članku predstavimo rodovne funkcije več spremenljivk, rekurzivne relacije in zaprte formule za določanje števila simetričnih in asimetričnih vrhov nepadajočih Dyckovih poti. Uporabimo tudi Riordanove matrike za študij šibko simetričnih vrhov, to je tistih, pri katerih je dolina pred naslednjim vrhom najmanj na taki višini kot dolina, ki temu vrhu sledi"}],"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-UVH09HRJ","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:DOC-UVH09HRJ"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:DOC-UVH09HRJ/8db13e6e-7e0f-47aa-8cf3-8c5cfa84e756/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-UVH09HRJ/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:DOC-UVH09HRJ"}}}}