{"?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-89JK2ICD/e4b16317-ba1a-4acb-a9be-27062910af26/PDF","dcterms:extent":"400 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-89JK2ICD/53570f19-975c-4135-9331-3aeb66661a4f/TEXT","dcterms:extent":"71 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-89JK2ICD","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2020","dc:creator":["Bucher, Eric","Machacek, John","Runburg, Evan","Yeck, Abe","Zewde, Ethan"],"dc:format":[{"@xml:lang":"sl","#text":"letnik:19"},{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"str. 249-275"}],"dc:identifier":["ISSN:1855-3974","COBISSID_HOST:44424195","URN:URN:NBN:SI:doc-89JK2ICD"],"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":"cluster algebra"},{"@xml:lang":"en","#text":"direct sum"},{"@xml:lang":"sl","#text":"direktna vsota"},{"@xml:lang":"sl","#text":"klasterska algebra"},{"@xml:lang":"sl","#text":"maksimalno zeleno zaporedje"},{"@xml:lang":"en","#text":"maximal green sequence"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Building maximal green sequences via component preserving mutations|"},"dc:description":[{"@xml:lang":"sl","#text":"We introduce a new method for producing both maximal green and reddening sequences of quivers. The method, called component preserving mutations, generalizes the notion of direct sums of quivers and can be used as a tool to both recover known reddening sequences as well as find reddening sequences that were previously unknown. We use the method to produce and recover maximal green sequences for many bipartite recurrent quivers that show up in the study of periodicity of ?$T$?-systems and ?$Y$?-systems. Additionally, we show how our method relates to the dominance phenomenon recently considered by Reading. Given a maximal green sequence produced by our method, this relation to dominance gives a maximal green sequence for infinitely many other quivers. Other applications of this new methodology are explored including computing of quantum dilogarithm identities and determining minimal length maximal green sequences"},{"@xml:lang":"sl","#text":"Vpeljemo novo metodo, ki daje tako maksimalna zelena, kakor tudi rdečeča zaporedja v tulcih. Ta metoda, ki se imenuje \"mutacije, ki ohranjajo komponente\", je posplošitev ideje direktne vsote tulcev. Uporabimo jo lahko kot orodje za rekonstrukcijo znanih in za iskanje še neznanih rdečečih zaporedij. Metodo uporabimo za rekonstrukcijo maksimalnih zelenih zaporedij pri številnih dvodelnih ponavljajočih tulcih, ki jih dobimo pri študiju periodi čnosti ?$T$?-sistemov in ?$S$?-sistemov. Poleg tega pokažemo, da je naša metoda povezana s pojavom dominance, ki ga je pred kratkim obravnaval Reading. Za poljubno maksimalno zeleno zaporedje, ki ga daje naša metoda, zveza z dominanco daje kakšno maksimalno zeleno zaporedje za neskončno mnogo drugih tulcev. Uporabe te nove metode, ki jih obravnavamo, vsebujejo računanje kvantnih dilogaritemskih indentitet in določanje maksimalnih zelenih zaporedij minimalne dolžine"}],"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-89JK2ICD","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-89JK2ICD"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-89JK2ICD/e4b16317-ba1a-4acb-a9be-27062910af26/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-89JK2ICD/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-89JK2ICD"}}}}